# Tutor profile: Timothy C.

## Questions

### Subject: Geometry

Angle A and Angle B are supplementary angles. If Angle A measures 60 degrees and Angle B measures 2x + 30 degrees, solve for x.

In math, we call two angles supplementary angles when their measures both add up to 180 degrees. If Angle A and Angle B are supplementary angles, and we know Angle A is 60 degrees, we can find out the measure of Angle B by taking 180 degrees - 60 degrees = 120 degrees. We know Angle B measures 2x + 30 degrees as well. If Angle B measures 120 degrees and also measures 2x + 30 degrees, we can say 2x + 30 = 120. We need to find the value of x which makes 2x + 30 = 120. When solving for equations, our goal is to have the variable alone on one side and we want to undo our order of operations, or PEMDAS, backwards. This means, we will start with any addition and subtraction. In my equation, I can undo + 30 by subtracting 30 on both sides. Doing so, we can rewrite our equation as 2x = 90. Our last step to having our variable x alone on one side is to eliminate the 2 in front of x. In math, when a number is in front of a variable, the number and the variable are being multiplied. Therefore, 2x means 2*x. To undo multiplication, we divide, so we can divide both sides of our equation by 2 to eliminate the 2. By dividing both sides by 2, this leaves us with x = 45, as 90 / 2 = 45. Therefore, if Angle A and Angle B are supplementary angles, then x = 45 degrees.

### Subject: Pre-Algebra

Evaluate the expression 15 - 2 * 3^2 / 6.

Math is a language used to communicate, and there can be multiple ways of interpreting something. In order to create consistency in communication, mathematicians for centuries have agreed to evaluate expressions from left to right and by following the order of operations. A quick way to remember the order of operations is PEMDAS, which tells us to first evaluate anything inside of parentheses first, then evaluate any exponents, moving on next to any multiplication and division, and finally any addition and subtraction. We will use PEMDAS to help us evaluate our expression. Starting off with P for Parentheses, the are actually no parentheses in our expression. Therefore, we can move on to E for Exponents. There is an exponent in our expression (3 ^ 2). Exponents are a way of communicating how many times to multiply a number by itself. 3 ^ 2 is telling us to multiply the number 3 by itself 2 times, so 3 * 3 = 9. Since 3 ^ 2 = 9, we can now rewrite our expression as 15 - 2 * 9 / 6, With exponents taken care of, we can move on to M for Multiplication and D for Division. Moving from left to right, the first thing I see is 2 * 9, and 2 * 9 = 18. I can rewrite my expression as 15 - 18 / 6. I notice there is division in my expression, too (18 / 6). 18 / 6 = 3, so I write my expression as 15 - 3. Finally, we can move on to A for Addition and S for Subtraction. Since there is no addition, we can move on to subtraction and the only thing we need to is evaluate 15 - 3, which 15 - 3 = 12. Therefore, we can say our expression 15 - 2 * 3^2 / 6 = 1.

### Subject: Algebra

Solve the equation 3x + 1 = 7.

You can think of equations like a balance scale. Both sides are evenly balanced and we want to keep them balanced at all times. If we are going to do something to one side of the scale, we must do the same to the other side. We can interpret this equation as the left side of the balance scale having 3 bags of coins (3x) and 1 coin, and the right side of the balance scale having 7 coins. Our goal is to find out how many coins are in each of the three bags. In order to start working towards our goal, we need to narrow our scale down to where one side is just bags and the other side is just coins. One thing we can do is remove the 1 coin on each side of the balance scale (-1 on each side). This leaves us with 3 bags of coins (3x) on the left side and 6 coins on the right side. If 3 bags of coins (3x) balance with 6 coins, if we can find a way to distribute those 6 coins evenly among the 3 bags (3x), then we can figure out how many coins are in each bag (x). With 6 coins and 3 bags (3x), I can split those 6 coins evenly into the 3 bags (3x) by having 2 coins in each bag (x). Therefore, I know each bag (x) will have 2 coins and I can say x = 2 is the solution to my equation.