Tutor profile: Puthita K.
Simplify this expression: 2x + 3(x + 5)
In this problem, we need to follow the order of operations. Some schools use PEMDAS or BEDMAS (or a variation of the sort) to help you remember the order of operations. PEMDAS means Parenthesis, Exponent, Multiplication or Division (which ever comes first from left to right), and Addition or Subtraction (which ever comes first from left to right). According to the order of operations, we need to get rid of the parenthesis first. In order to do that, we need to use the Distributive Property, which states: a(b+c) = ab + ac This is our original expression: 2x + 3(x + 5) This is after we use the distributive property on the 3(x + 5) part: 2x + (3)(x) + (3)(5) 2x + 3x + 15 Now, next down the list is addition. Here, we can see that we can combine the 2x and the 3x because they have the same degree (or "last names"): 5x + 15 Since there are no more terms with the same degree, 5x + 15 is in its simpliest form and is, therefore, our answer.
Subject: College Admissions
Colleges/universities are too expensive. What do I do?
Depending on what major(s) you're interested in, size of the school that you want, and location that you want, you have a lot of options in terms of alleviating the costs. To get into specifics, I would need to get to know more about who you are and what your interests are in order for me to properly tailor this answer for your situation. Here are some key thoughts: Why are you going to college/university? What does it mean to you to go to college/university? What is your dream job? How can a degree help you get that dream job? We need to work backwards in order to help you get the most out of your money. Some graduate schools don't recognize certain degrees, so if your dream job requires a graduate degree, then look at the graduate schools' bachelor's degree requirements first. This not only includes type of degree but also accreditation. Accreditation is how schools get graded or confirmed by certain organizations. Some accreditations are almost meaningless, and these colleges/universities are considered money mills. Of course, top universities have the proper accreditations. What type of degree(s) do you need? What is your preferred size of college/university? There are small colleges/universities that have under 3000 students while some are as large 50,000+ students. This affects class sizes, number of scholarships given out, tuition fees, jobs availabilities, future opportunities, and so much more. Hence, you'll need to be real about what you need in terms of size. This is going to be around four years of your life for a bachelor's degree, or more if you decide to get a dual-graduate degree in a fast track. Do not torture yourself at a too small school for you since facilities, opportunities, and friends can be limited. Do not torture yourself at a too big of a school for you either since class sizes can be huge. If you need smaller class sizes, a big school most likely won't have that. Improper college/university sizes for you can be draining, which can result in under performing in your classes. And if you do receive scholarships from this college/university, there might be a GPA clause that may result in you not being able to further receive those scholarships. Hence, take the time to figure out what the student to faculty ratio that you need and if you want to be in a huge school or not. It will affect your costs. What is your preferred location of college/university? Small town/Huge city Cold weather/Warm weather/mixed of both/ideal temperature Does it have to be in a certain country? Here are some general answers: First, let's define financial aid: financial aid is composed of all money that is available to you for college/university This can include your income, part of your parents' income/assets, scholarships, grants, and loans. What affects your financial aid package directly: -socioeconomic status -your interests (this is why we need to figure out which degree you need first) What affects your college/university admissions and in turn, also your financial aid package: -test scores -grades -personal statement -ratio of difficulty of classes taken to availability of difficult classes at your school -community service/internships/other extracurricular activities -rank in school -rank of school -letters of recommendations We need to figure out what you already know and bust some of the myths of colleges/universities before we can find out the best way for you to go to college/university on your budget. We can discuss these key thoughts and more. I'll show you exactly how to put your best foot forward in my 20 hours course.
Solve for x: 9x + 5 = 8
The full explanation (the long answer...short answer below): To solve for x, we're basically asking for any value(s) that can be substituted in for x to make the equation hold true. For example, 4=4 is true while 7=5 is untrue because 7 is not equal to 5. Let's say we choose 5 for x. Does that make the equation hold true? To see, we substitute in 5 for x. 9(5) + 5 = 8 Now, following the order of operations, we multiply 9 and 5 first. 45 + 5 = 8 Then, continuing the order of operations, we add 45 and 5, and we get: 50 = 8 Now, we know that 50 is not equal to 8, so the equation is untrue. That means the 5 that we substituted in for x is not the answer. We can keep guessing and checking like this until we find an answer, but that will usually take too long. Hence, we use a more systematic method called algebra. Algebra is basically a set of rules that we apply to solve for a missing value or values. In this case, it's x. So what are the rules to solving this equation? Let's refer back to when we were substituting in 5 for x to guess and check. We followed the order of operations. Some schools call this PEMDAS or BEDMAS (or a variation of the sort). PEMDAS stands for Parenthesis, Exponent, Multiplication or Division, Addition or Subtraction. This means that we always do parenthesis first, then exponent, then multiplication or division (which ever comes first from left to right), and lastly, addition or subtraction (which ever comes first from left to right). When we substituted in 5 for x to guess and check, there were only multiplication and addition, so that's why we multiplied first and then added. To put it simply (the short answer): In order to solve for x, we need to work backwards, meaning that we go in the reverse order of operations. What this means is that x wants to be left alone on one side of the equal sign like this: x = something or something = x That is our goal. Now, to move that something to the other side, we need to make sure that the equation stays equal. That's why when we move something (i.e. do an operation) on one side, we also have to do the same to the other side of the equation. But first, what is that something in this equation? What's bothering the x? Pretend that the x is anti-social. It wants to be left alone on one side of the equation. 9x + 5 = 8 Here, we can see that 9 and 5 are bothering the x on the left hand side (LHS) of the equation. We need to move the 9 and 5 to the other side of the equal sign somehow. To do that, we look at the operations 9 and 5 are doing to the x. Here, we can see that the 9 is multiplying the x and 5 is adding to the x. Now, the normal order of operations dictates us to do multiplication first and then addition, but since we're solving for x, we do it in the reverse order of operation: addition first and then multiplication. So 5 goes first and then the 9. In order to get rid of addition, we have to do subtraction, and what do we to one side, we have to do to the other: 9x + 5 = 8 - 5 -5 We get: 9x + 0 = 3 Since zero plus anything is itself, 9x = 3 Now, we get rid of the 9. Since 9 is multiplying the x, the opposite operation is dividing by 9. And again, what we do to one side, we do to the other to make sure the equation stays balance. (9x)/9 = (3)/9 That works out to: 1x = 3/9 Since one times anything is itself, x = 3/9 In answers in algebra, we always simply our fractions, and we usually either leave it as a proper or an improper fraction and not as a mixed number unless specified. Hence, in reducing 3/9, we get: x = 1/3 To recap: First: what's bothering the x? What's making x not be alone? Second: what are those bothering the x doing to the x? (what operations?) Third: what's the reverse order of operations? what needs to go to the other side first? Fourth: do the opposite operation to both sides. If it's adding, subtract. If it's dividing, multiply. etc. Answer: you will get x = something when you're done, but make sure it's in its simpliest form To check to see if the answer that you got is correct, simply substitute your answer back into the equation to see if it holds true. Let's check our answer, x = 1/3, together: 9x + 5 = 8 Substitute 1/3 for x: 9(1/3) + 5 = 8 Following the order of operations, we multiply 9 times 1/3 first to get: 3 + 5 = 8 Continuing the order of operations, we now add 3 and 5 together to get: 8 = 8 Since 8 is equal to 8, the equation holds true, which means 1/3 is indeed our answer (x = 1/3).
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