5 Strategies to Manage Introverts at Work - Introvert Whisperer

Introvert Whisperer / 5 Strategies to Manage Introverts at Work - Introvert Whisperer 5 Strategies to Manage Introverts at Work Emma Otusajo August 6, 2017 Adaptability, Communication, Leadership No responses Managing Introverts in the Workplace Your team is made up of many characters and every manager knows that although they can’t all be pleased at the same time, it is up to them to make them feel comfortable so that they can thrive in their job. Part of a manager’s job is to try different strategies to reach out to each staff member to make sure they are content, happy and given what they need to enable them to perform at their most productive. When considering whether staff have more of an extroverted or an introverted nature, this can impact on a manager’s approach to working with them and the working environment created. Happy staff means everyone gets more work done and that means the team is more productive â€" yes! The more flexible a manager can be with their approach the better â€" and staff will be grateful for these thoughtful approaches, too. So how, as a manager, can this be achieved? Learning a little something about what makes people introverted or extroverted can help. It all comes down to those brain chemicals we call adrenaline, which introverted people are highly sensitive to, as author Alen Mayer states in his book Introverts in Business: Being Quietly Successful. Extroverts, on the other hand, do not produce enough of the feel-good chemicals dopamine and adrenaline and are more likely to look for outward events that give them the uplifting feelings to raise their levels. This is why those staff who appear quieter don’t necessarily have a lack of ideas, while those who speak the most are not always right. Here are some practical suggestions to use at work to ensure more introverted staff are just as at ease and comfortable in the office as their colleagues: Let Employees Know Agenda in Advance and Write Down Ideas You’ve all been to at least one team meeting where 2 or 3 people dominate the entire conversation and you can’t get a word in. Then when your manager does ask you what you think, all you can draw is a blank because, as an introvert, ideas don’t come to you straight away. Before you know it, your colleagues are commenting about how quiet you are and your manager thinks their one quiet employee is not interested in the project. Managers can get around this by giving their team members time to think about the project in advance. Preparing an agenda ahead of time or simply letting your team members know what the topics will be will help and allow them time to come up with their own ideas, ready for the meeting. Praise and Criticism   When it comes to praising staff, a manager may think it’s great for everyone to be congratulated and recognised at the next team meeting by way of an official announcement, but get ready: Not everyone will be. While not all, many introverted staff will feel overwhelmed by suddenly being in the spotlight and overwhelmed by the spontaneous liveliness that takes place. Managers could try letting their staff know in advance that they are going to be mentioned at the next team meeting so that at least the employee has a chance to turn down the offer. An extrovert may appreciate praise from their manager when it is given in the presence of a team dinner or meeting. Introverts will much prefer and appreciate being praised on more of a one-to-one basis to let them know how much they’re valued. This is the same for giving constructive criticism â€" do it at the next appraisal or review meeting to give your introverted staff member time to think about it and respond. Communication in the Workplace   In an environment where there is pressure to get things done and to do tasks quickly, managers can often expect answers to their questions or demands to be given on tap. This is especially pressurising when a manager stands over your desk expecting you to find what they need or answer them straight away. When asking a question, a manager can give their staff time to run through their thoughts briefly or to find what it is you need, so that they don’t feel any undue pressure. Wait for them to finish speaking when they’re in the flow (which is worth it when they do) â€" interrupting them will throw them off track and they may not be able to finish making their point, or won’t feel that they have been listened to. Different Workspaces in Your Environment   With the introduction of open plan offices and hot desking, while for some it was an opportunity to interact with more people during the day and be more sociable â€" for the more introverted staff, it was more of a nightmare. For the introverts among us, entering an open plan office means more people looking up at you, as if you’re walking down a catwalk putting on a show you really don’t want to do. Even if you do seek out the comfort of a familiar face, any conversation you have carries out across the room! Managers, organise workspaces to allow for some small, more secluded spaces so that employees can have at least semi-private conversations and not feel like they are no show by anyone and everyone. This can consist of booths and small, partitioned offices that make staff feel like they’re not so much in the spotlight. Seeing Everyone’s Strengths   While it is important to enable time for introverted staff to have some quiet in the office or by themselves, it can be equally as important to plan team training or activities that bring all your colleagues together. Learning about one another’s differences and getting to each other on a more personal level is always going to be a positive when it enables staff to understand each other’s strengths, shown through the activities planned. An activity to build a raft together? That quiet girl who sits in the corner knows how to tie rope together so that the raft can be strong. Tasks outside of the office can also remind introverts to see the strengths of their extroverted colleagues â€" but do give them plenty of notice of the get-together first. Go to top OFFICE POLITICS Power-Influence-Office Politics: it comes down to your Strategic Relationships and understanding of how you build each one of these elements. I want to help you accelerate your career by connecting you with your Free Instant Access to my video that outlines all of this and meaningful actions you can take today!  Start watching now by clicking here! Brought to you by Dorothy Tannahill-Moran â€" dedicated to unleashing your professional potential. Introvert Whisperer

The Introverts Guide to Enjoying Solo Travel - Introvert Whisperer

Introvert Whisperer / The Introverts Guide to Enjoying Solo Travel - Introvert Whisperer The Introverts Guide to Enjoying Solo Travel Solo travel is a remarkable thing to enjoy. It’ll allow you to explore the world freely without relying on the company of anyone else.   However, it can prove to be quite a challenge for introverts as you may be reluctant to meet other people and join in with group activities.   If that’s the case; here’s the introvert’s guide to enjoying solo travel.   Explore beyond your comfort zone One great way to enjoy solo travel as an introvert is to explore the areas beyond your comfort zone.   While this may seem like an entirely daunting prospect at first, you’ll soon see developments and improvements in your confidence levels and people skills.   Any activity that you wouldn’t usually participate in, such as kayaking, mountain climbing or bungy jumping for example, will really push you out of your comfort zone and help to build your confidence massively. It will also show you that you’re much more capable of things than you first thought, which will only aid you when it comes to future solo travel trips.   Immerse yourself in nature a lot Immersing yourself in nature is such an ideal way to enjoy solo travel as an introvert.   Spending time in nature in places such as the beautiful Scottish Highlands really allows you to reconnect with yourself and become one with your surroundings. Walking in the Scottish Highlands is the perfect place to do this as you can enjoy the peace and quiet and enjoy spending some quality time with yourself.   Even if you only go for a walk through the local park in the city that you’re visiting, you can really try to reconnect with yourself and enjoy the beautiful scenery and tranquillity that nature offers.     Pluck up the courage to ask someone to take your picture As a notorious introvert, you may be incredibly shy when it comes to asking people, especially strangers, for a favour but as a solo traveller, this is an incredibly effective way to ensure you’re enjoying yourself.     Something as simple as asking someone to take your picture can be a great way to embrace solo travel and ensure that you document all your experiences. While taking your own pictures of all the landscapes and cityscapes that you’ve seen is amazing, you also need to make sure you’ve got plenty of pictures of yourself too!   Most people will be more than happy to help you out and take your picture, especially if they recognise how much of a big deal it was for you to go out of your way to ask them.   Sit near the bar at restaurants Another great way to enjoy solo travel as an introvert is to sit at the bar at restaurants. While it may seem like an odd thing to suggest, it’s actually a great tip to bear in mind when you’re solo travelling as an introvert.   This is because a seat at a table in the middle of a busy restaurant can feel quite overwhelming and intimidating, especially when you’re eating alone.     However, by sitting at the bar, you’ll have a great view of the ambience and vibe of the restaurant, without being in the middle of all the hubbub. It’ll also mean that you won’t have to feel too awkward when ordering your food as you’ll be close to the staff and waiters who can easily and comfortably take your order.   Take advantage of group tours As an introvert, you’re much more likely to want to spend the majority of your time alone when travelling.   However, a great way to enjoy your solo travel trip even more is to join group tours. You’ll get the chance to meet lots of new people, see things you might not have otherwise seen and it’s also a great opportunity to push yourself out of your comfort zone.   There are so many amazing group tours to take advantage of. Whether you want to join a group tour of an entire country, city or just an excursion, they can be an incredible way to enhance your solo travel experience even more.   Conclusion Enjoying solo travel comes in many different forms and variations. Each individual experience of solo travel pertains to each person but by following the steps above, you’re much more likely to enjoy your time solo travelling as an introvert.   Ensure you push yourself out of your comfort zone when travelling and try to join group tours when you can to give yourself the chance to meet new people and gain new experiences.     Immersing yourself in nature as much as you can is also a great way to enjoy solo travel as you’ll be able to take yourself off for long walks and enjoy the beautiful views and scenery.   Author Bio: Rebecca is a translator by day, and a traveler mostly at night. She is an expert on living with jet lag â€" and packing in tiny suitcases. You can read more of her exploits at RoughDraft. Go to top Do you know what your next career step is?   Many people don’t. I want to help you accelerate your career by connecting you with your Free Instant Access to my eBook on how to construct your Career SMART Goals â€" that will help you put together your actions and keep you accountable. Get your copy now and start your action plan today! Brought to you by Dorothy Tannahill-Moran â€" dedicated to unleashing your professional potential. Introvert Whisperer

Everything You Need to Know About the Blues Scale on Guitar

Everything You Need to Know About the Blues Scale on Guitar Sign up successful What is the Blues Scale? In its simplest form, the blues scale is simply a pentatonic scale. That might sound complicated, so lets break down the theory. Look at a piano if you have one, or look up an image of piano keys. Take a look at the black keys on the piano. They naturally fall into the pentatonic scale pattern. If you want to hear the pentatonic scale in the easiest way, just play anything you want on the black keys only. The gaps between the groups of black keys show you something very important about the scale. Some of the notes are farther apart than others. This is because there are two types of “intervals” (or, spaces between notes) in the pentatonic scale. There are whole steps and minor thirds. The whole step is made up of two half-steps. This is also equal to two frets on the guitar. The minor third is made up of three half-steps, which is equal to three frets on the guitar. Whole steps and minor thirds are also referred to as “steps” and “skips.” Being aware of this pattern of steps and skips is the most important aspect of learning the blues scale. Practice with the Pentatonic Scale Let’s put the theory weve just learned into practice. The main resting or finishing note of a key is called the “root.”   As an example, we’ll look at the key of A minor. In the key of A minor you have the notes A C D E G. Those would be all natural notes (with no sharps or flats) and all white keys on a piano. In any key you make a pentatonic scale in, you start with the root and go up a minor third (three half steps), then a whole step, then another whole step, then one more minor third, then one last whole step. So in the key of A minor, the interval pattern from the root  is: (A) Skip (C) Step (D) Step (E) Skip (G) Step (A) The same interval pattern would apply to any key, so even if the notes change, the sound of the scale will be similar. In other words, the interval structure is what determines most of the mood of a scale. When you go to learn this on the guitar, the main thing you will learn to do is memorize “boxes” or patterns of whole steps and minor thirds that go across the strings. We will talk about these more in the next section, but realize that it is an incredibly important and fundamental exercise to master at least one pentatonic box that you can use for playing songs. Difference Between the Pentatonic Blues Scales The main difference between the blues scale and the pentatonic is the addition of one note. In the whole step between the third and fourth notes, you will play the note that falls between the third and fourth notes. For example, in A minor, you’ll add an Eb in between D and E. So the interval pattern for the blues scale in the key of A minor would look like: A (Skip) C (Whole Step) D (Half Step) Eb (Half Step) E (Skip) G (Whole Step) A The reason this extra note is present is because it has a special place in a lot of blues melodies. It’s important to mention that it’s not enough just to have the extra note in the scale. The way you use it to create the blues sound is to play it in blues licks. The best way to understand this is to learn the scale, and then play songs that use it so you can see the way it gets applied. Playing the notes of the blues scale in totally random ways does not produce a “bluesy” sound; only playing the scale in the way it shows up in the traditional canon of songs will get you to the right place as a blues guitar player. RELATED: 5 Easy Blues Guitar Licks The Blues Scales in Common Keys When you start out learning the blues scale on guitar, you will want to learn the scale in the most common keys that it’s played in. Let’s start with the E blues scale. E Blues Scale This scale is usually considered the easiest to start with because it uses open strings and gives your fingers more time to adjust to changes. Source: Total Guitar and Bass In tablature, it will look like this. Source: National Guitar Academy If you want to play in most of the keys of the blues though, you need to learn the scale in a position that doesn’t use any open strings A Blues Scale The thing that is so nice about the guitar is this: once you know this shape, all you have to do is move it around to the key you want to play in! Source: Online Guitar Books Here is what the A blues scale looks like in tablature.   Source: Online Guitar Books Here are charts and tabs for two more of the most common keys. Give them a try and see if you can transfer the shape just by finding the root/starting note on your thick E string. G Blues Scale Source: ThoughtCo. Source: Online Guitar Books C Blues Scale Source: Guitar Command Source: SimplifyingTheory.com Practicing the Blues Scale on Guitar Practice these scales in a way that inspires you. There are plenty of fun ways to master the blues scale on guitar, and you should choose the ones that inspire you the most. Remember: motivation comes from action! Here are a few ideas to get you started. Repeat the A minor blues scale from the lowest note to the highest note, and then back down until you can remember the notes in order without looking at a tab or diagram. Switch between reading the diagram and then trying to remember, to see where your memory has gaps. Play one note at a time in the scale, along with a metronome at 60 BPM. Try to remember the finger pattern while playing with your eyes closed. Open your eyes to look only if you get lost. Pick a random song and try to place the scale shape you learned on the root note. You can try different notes until you find the root by ear, or look up the key of the song and place the scale box on that root. Knowing the blues scale is like knowing the alphabet, and life is a lot better when you can spell! This scale gets used with specific licks and phrases that define the blues sound, and having a teacher to help you see the connection between the scale and the music can be very helpful. If you would like to find someone to help you take your blues skills a step further, look for a guitar teacher at TakeLessons. A local or online teacher will help you stay motivated as you progress, and give you more fun ways to practice all you’ve learned! Post Author: Jonathan B. Jonathan B. teaches blues guitar, bass, and more in State College, PA. Jonathan is a Temple University, Music Theory graduate and YouTube celebrity with thousands of subscribers.  Learn more about Jonathan here! Need Private Lessons? Search thousands of teachers for local and live, online lessons. Sign up for convenient, affordable private lessons today! Search for Your Teacher

Why The Arts Are Crucial To Education

Why The Arts Are Crucial To Education Save the arts thats the mantra of many educators. But, after all, it could be the arts that save us. Funding for arts education is consistently cut and decreased when budgets become tighter. Some administrators and educators dont believe its as important as other subjects, and its incredibly more difficult to measure the effects of an arts program. But, a presidentially-appointed committee on arts education is trying to change the perception of arts education, according to an article in the Washington Post. The committee is arguing that arts education can help students at all levels find their voice and have a better sense of their skills. However, the committees main argument is that arts education can actually improve students achievement in all subjects. Obamas Committee on the Arts and the Humanities recently released a report, Reinvesting in Arts Education: Winning Americas Future Through Creative Schools. The report is the first federal analysis of arts education in more than 10 years, and it took the committee 18 months to analyze the data. The report boils down into these five recommendations for arts education. Build robust collaborations among different approaches to arts education Develop the field of arts integration Expand in-school opportunities for teaching artists Utilize federal and state policies to reinforce the place of arts in K-12 education Widen the focus of evidence gathering about arts education The report's claim that arts can improve achievement in all areas caught the education worlds attention. Right now, educators are obsessed with improving students test scores. So, they are listening to anyone and anything that could possibly help test scores. The report didnt wait long to argue that more arts education will improve test scores. It jumps straight to that subject in one of the first few paragraphs of the 76-page analysis. The report also argues that more arts education will improve students motivation, engagement, persistence, class attendance and enhanced problem solving, creativity, social skills and multitasking. The report goes through great lengths to prove its claims most of which simply stem from the basic concept that engaging in creative activities helps improve and increase cognitive abilities, which then leads directly to better test scores and achievements.

9 Cooking Blogs To Follow For Amazing French Recipes

9 Cooking Blogs To Follow For Amazing French Recipes Megan L. One of the best things about learning to speak French is the opportunity to enjoy amazing French food! Even if you dont have plans to travel to France anytime soon, you can still take a culinary journey in your own kitchen. These nine French cooking blogs are absolute must-follows for foodie francophiles! Check out classic French recipes, contemporary takes on traditional flavors, and soak up a bit of French culture. Everyday French Chef Think you dont have time to prepare authentic French recipes? Think again! The Everyday French Chef  can teach you how to make delicious French food without spending all day slaving in the kitchen.    Written with normal working people in mind, this fabulous blog simplifies the art of cooking fine French cuisine. We recommend:  Sole Meunière Thanks to The Everyday French Chef, you can make this classic French dish in just minutes. Its perfect for a romantic dinner for two. French Girl Cuisine The author of French Girl Cuisine is Natacha Gajdoczki, a French girl living and cooking in Switzerland. Her recipes range from quick and simple for beginning chefs to more challenging dishes for kitchen wizards. She also occasionally mixes in flavors from other neighboring European countries. One thing that all her recipes have in common is how delicious they look! We recommend: Blueberry Tart Cook up this fresh and beautiful dessert to impress dinner guests, or keep it for yourself. French Revolution Food The author of French Revolution is a native New Yorker who takes inspiration from her French mothers cooking as well as American cuisine. Describing her recipes as French-American Fusion, she shares recipes that are simple and flavorful, and always come with a fun story to set the scene. We recommend: Summertime French Country Deviled Eggs Chocolate and Zucchini Looking for fresh, modern, and seasonal French recipes? Written from her Parisian kitchen, Clotilde Dusouliers blog Chocolate and Zucchini is precisely what youve been searching for. This modern French cooking blog highlights recipes that are both simple and delicious, as well as being great for cooks at all levels. We recommend:  Raw Chocolate Hazelnut Truffles Who doesnt love a little sweet treat? Roll up these little truffles by hand to impress your friends or a special someone. My French Kitchen My French Kitchen is a beautiful, artistically done French cooking blog that encourages creativity and experimentation in the kitchen. Based in Touraine, this blog explores traditional French flavors and is sure to inspire you to be freer and more imaginative in your cooking. Along with the beautiful food photography, My French Kitchen also often features lovely watercolor illustrations and photographs of French life. We recommend:  Carrot and Poppyseed Cupcakes These cupcakes are fresh and sweet, and extra moist because theyre made with yogurt. French Cooking for Dummies Who are you calling dummy?!? Actually, appreciating the fantastic ease and simplicity of these French recipes doesnt make you a dummy at all! Based in Paris, the author of French Cooking for Dummies aims to uncomplicate classic French cooking. With her help, anyone who wishes to try their hand at French cuisine is sure to succeed. We recommend: Warm Goat Cheese Salad This classic French bistro salad makes a delicious lunch, taking advantage of the amazing  natural flavors of goat cheese and arugula. On Rue Tatin Although she is based in France, the author of On Rue Tatin has a worldwide appreciation for both where food comes from and how it is prepared. If youre looking for French recipes that are more than just food, this is the blog for you. Explore customs and learn about the meaning of these delicious dishes. We recommend:  Strawberry Shortcake à la Française In spring when strawberries are fresh, this classic dessert is exceptionally delicious! The Flo Show Looking for a globetrotting French chef? Look no further than The Flo Show! This French native shares her internationally-inspired dishes alongside traditional French favorites. For a French spin on world cuisine, this blog simply cant be beat. We recommend: 2-Ingredient Chocolate Mousse How can something this delicious and fancy have only two ingredients? You wont believe how simple and delightful this recipe is. The Vegan Version In traditional French cooking, vegans have very few options among the meats, cheeses, and cream sauces that make up many French dishes. Seeking to correct this disparity, the author of The Vegan Version  is working her way through Julia Childs classic recipes and veganizing them.    If youre vegan, vegetarian, or just adventurous in the kitchen, youre sure to find intriguing new takes on old French recipes. We recommend: Bouillabaise A vegan version of this traditional fish soup is actually possible, and not that complicated to make. Youll be amazed by the authentic flavor! What are some of your favorite French recipes? Share them with us in the comments below! Interested in Private Lessons? Search thousands of teachers for local and live, online lessons. Sign up for convenient, affordable private lessons today! Search for Your Teacher

Yikes! Dont Confuse These 7 Tricky Spanish Words

Yikes! Dont Confuse These 7 Tricky Spanish Words Suzy S. As a beginner learning Spanish, its easy to feel overwhelmed by new vocabulary. How do you keep track of all of the Spanish words and meanings? Not to mention all the false cognates that  are out there! Fortunately, with practice, Spanish words and phrases  will become like second nature to you. Just watch out for the tricky word pairs! For a helpful lesson,  our friends at Lingolistic  recently shared an article with us  with some words that are particularly confusing for beginners. Here are a few of them: Vaya, valla Vaya: to indicate surprise, either for a bad or a good reason. It also works as the verb “to go,” which is where most people make mistakes. Example: “ ¡Vaya noche, me lo he pasado genial!” (What a night, I had a wonderful time!). Valla: it sounds the same, but it means “fence.” Example: “Ayer pinté la valla de verde” (I painted the fence green yesterday). So  remember: vaya for the verb, valla for the object. Haber, a ver Although the difference is quite big, people tend to make this mistake very, very frequently since both sound the same. Haber: the verb to indicate “there is” or “there are.” Example: “Hay un coche estropeado” (There is a broken car there). A ver: the meaning is “let’s see,” but people usually use the previous verb (haber) instead. Example: “A ver, qué comemos hoy” (Let’s see, what do we have for lunch). Ay, hay, ahí If youre a Spanish learner, this might be a headache, but don’t worry, there is a sentence to make it clearer: “Ahí hay un hombre que dice ¡ay!” (Over there, there is a man saying ouch!). Ahí: “there, over there” Hay: the verb “haber” in present  tense, “there is/are” Ay: a moan, “ouch” Continue reading the article here, and make sure to check out the other resources Lingolistic  has available for Spanish learners! Readers, what other word pairs do you get confused? Ser vs. estar is another one our tutors have pointed out. Let us know what Spanish words and meanings you struggle with by leaving a comment below!   Interested in Private Lessons? Search thousands of teachers for local and live, online lessons. Sign up for convenient, affordable private lessons today! Search for Your Teacher

High-Poverty Charlotte Schools Gets Boost From Duke Energy

High-Poverty Charlotte Schools Gets Boost From Duke Energy Math Tutoring At High-Poverty Charlotte Schools Gets Boost From Duke Energy Math Tutoring At High-Poverty Charlotte Schools Gets Boost From Duke Energy June 3, 2015 Heart is thrilled to share that we are expanding our programs in Charlotte-Mecklenburg Schools, thanks to a $8,000 grant from Duke Energy Foundation. “Math skills that students learn at a young age serve as a foundation block for their entire education career,” said Stick Williams, Duke Energy Foundation president. “Those skills advance other academic pursuits and help our young people meet and overcome new challenges as they prepare for the future.” “Lack of math proficiency can become a barrier to a student’s academic confidence,” said Emily Elliott, executive director of Heart Math Tutoring. “Math deficiencies also affect high school graduation rates and future job opportunities.” The Duke Energy Foundation grant will support program expenses at one of our  school sites, where 50 students, in grades 1-5, receive one-on-one instruction from a volunteer. “We’re very excited that Duke Energy Foundation has chosen to support Heart, and we’re encouraged by the shared focus on K-12 education for underrepresented groups, particularly in the areas of math and science,” Elliott said. “Financial contributions like Duke Energy’s make it possible for us to do this important work.” Read the full press release here.

SAT Math Solving Impossible Math Problems

SAT Math Solving Impossible Math Problems ACT SAT Prep and College Admissions Blog The SAT sometimes approaches math a bit differently than we’re used to in math class. One of these differences in approach is in the way some SAT math problems ask us to solve for relationships between variables, rather than the value of one particular variable. These problems can seem very challenging, or even downright impossible, at first glance, because they often give us multiple variables but only one equation. One thing we learn in math class when studying systems of equations is that in order to solve for 2 variables, we usually need 2 separate equations; to solve for 3 variables, we need 3 separate equations; and so on. Certain SAT math problems will appear to violate that general rule and ask us to do something that’s supposed to be impossible, like solving for 2 variables with only 1 equation. When we look more closely at such problems, though, we realize that the SAT is not really asking for the value of each individual variable involved. Instead, we’re asked to find the value of the sum, product, or some other relationship involving 2 or more variables. Let’s look at an example of such a problem: If 4x + 7y + 1 = y â€" 2, What is the value of 2x + 3y? A. -2 B. -1.5 C. -0.5 D. 2 E. 4.5 Explanation and solution: We’re given only one equation, but it involves 2 unknowns: x and y. We really don’t have enough information to solve for the value of x and/or the value of y, but fortunately, that’s not what the question asks us to do. Instead, we are asked to find the value of a sort of relationship that involves both x and y together: 2x + 3y. To do this, we algebraically manipulate the equation that’s given. Instead of trying to isolate x or isolate y, we try to isolate the quantity “2x + 3y”. To do this, we can first subtract y from both sides of the equation, and then subtract 1 from both sides, so that the equation now looks like: 4x + 6y = -3. To finish isolating “2x + 3y”, we divide both sides of the equation by 2 and obtain: 2x + 3y = -1.5. So the correct answer choice is “B”. Let’s look at another example: If the average of x, y, and z is 12, what is the value of 3(x + y + z)? A. 12 B. 24 C. 36 D. 72 E. 108 Explanation and solution: To obtain the average of x, y, and z, we would need to add the 3 numbers together and then divide the resulting sum by 3. Since we are told that their average equals 12, we can express the information as an equation: (x + y + z)/3 = 12. Multiplying both sides of the equation by 3, we obtain: (x + y + z) = 36. To find the value of 3(x + y + z), we can again multiply both sides of the equation by 3 and find that 3(x + y + z) = 108. The correct answer choice is “E”. Notice that in the problem we just solved, we did not solve for the individual values of x, y, or z; that would have required more information than we were given.