Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 2 Please watch Section 16 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item67.cfm Page 1
1) Find x. 2) Find x. Page 2
3) Find y. 4) Find y. Page 3
5) Find n. 6) Find j. Page 4
7) Find x. 8) Find x. Page 5
9) Find x. 10) Find y. Page 6
11) Find n. 12) Find x. Page 7
13) Find y. 14) Find x. Page 8
1) Find x. When solving an equation for a variable, the goal is to get the variable, x, by itself. We can isolate x by subtracting 16 from the left side of the equation. Remember, everything we do to one side of an equation, we need to do to the other, so we also subtract 16 from the right side. We then complete the arithmetic and arrive at our solution. Page 9
2) Find x. When solving an equation for a variable, the goal is to get the variable, x, by itself. We can isolate x by adding 9 to the left side of the equation. Remember, everything we do to one side of an equation, we need to do to the other, so we also add 9 from the right side. We then complete the arithmetic and arrive at our solution. Page 10
3) Find y. When solving an equation for a variable, the goal is to get the variable, y, by itself. We can start to isolate y by subtracting 20 from the left side of the equation. Remember, everything we do to one side of an equation, we need to do to the other, so we also subtract 20 from the right side. After simplifying, we are still left with y on one side of the equation. To cancel the negative sign in front of y, we can divide each side by -1. The negative signs cancel out and we are left with y isolated, and have found our solution. Page 11
4) Find y. When solving an equation for a variable, the goal is to get the variable, y, by itself. We can start to isolate y by subtracting 9 from the left side of the equation. Remember, everything we do to one side of an equation, we need to do to the other, so we also subtract 9 from the right side. 9 y 9 = 15 9 y = 6 y 1 = 6 1 y = 6 9 y = 15 y = 6 After simplifying, we are still left with y on one side of the equation. To cancel the negative sign in front of y, we can divide each side by -1. The negative signs cancel out and we are left with y isolated, and have found our solution. y = 6 Page 12
5) Find n. When solving an equation for a variable, the goal is to get the variable, n, by itself. We can isolate n by dividing the left side of the equation by 6. Remember, everything we do to one side of an equation, we need to do to the other, so we also divide the right side by 6. We then simplify and complete the arithmetic. With n isolated and simplified, we have found our solution. Page 13
6) Find j. When solving an equation for a variable, the goal is to get the variable, j, by itself. We can start to isolate j by dividing both sides of the equation by 8. With j isolated and simplified, we have our solution. Page 14
7) Find x. When solving an equation for a variable, the goal is to get the variable, x, by itself. To isolate x, we need to multiply the left side of the equation by something that will cancel any numbers on the x side of the equation. In this problem, we can multiply both sides of the equation by 2/3. Working on the left side of the equation, we can see the 2 s and 3 s cancel, leaving x isolated. We can also cancel a 2 from the top and bottom of the right side of the equation as well. The multiplication can then be completed. With x isolated and simplified, we have our Page 15
solution. Page 16
8) Find x. When solving an equation for a variable, the goal is to get the variable, x, by itself. Since the variable is divided by 3, we must multiply both sides of the equation by 3. The 3 s on the left side of the equation cancel, and we have isolated x. On the right side of the equation, we can cancel a 3 from the top and bottom of the equation, since we know 3 is the same as 3/1. After the cancellation, we re left with 2/1 which is the same as 2. With x isolated and simplified, we have our solution. Page 17
9) Find x. When solving an equation for a variable, the goal is to get the variable, x, by itself. The easiest way to solve for x in this problem is to first get x to the numerator of the fraction. One way to do this is to multiply both sides of the equation by x. We previously have always moved only numbers around by adding, subtracting, multiplying and dividing. Remember, variables are just numbers that we don t yet know, so the same rules apply. We can do all the same operations, as long as we do the same thing to both sides of the equation. The x s on the left side of the equation cancel (since x is the same as x/1) and we have x in the numerator on the right side. Now we simply divide both sides of the equation by 3 to isolate x. 6/3=2. Even though we are used to seeing the variable on the left side of the equals, we have still isolated the variable. It s often easiest to read if we just flip the order. It s still the same answer. With x isolated and simplified, we have our solution. Page 18
10) Find y. When solving an equation for a variable, the goal is to get the variable, y, by itself. To isolate y, we can multiply each side of the equation by 5/3. On the left side of the equation, the 3 s and the 5 s cancel and we re left with y isolated. On the right side of the equation, we can cancel a 3 from the top and bottom. Further simplification gives us our solution. With y isolated and simplified, we have our solution. Page 19
11) Find n. When solving an equation for a variable, the goal is to get the variable, n, by itself. The first step to isolate n is to subtract 3/4 from both sides of the equation. Simplifying, we re left with n isolated. On the right side of the equation, any number subtracted from itself is 0. With n isolated and simplified, we have our solution. Page 20
12) Find x. When solving an equation for a variable, the goal is to get the variable, x, by itself. The first step to isolate y is to multiply both sides of the equation by -8/5. On the left side of the equation, the 5 s, 8 s and negatives cancel, leaving x isolated. On the right side of the equation, the negatives cancel and we can divide the top and bottom by 4 to start to simplify our answer. Next, we multiply the remaining fractions. Since 6/5 is an improper fraction, we can convert it to a mixed fraction as we have done in previous lessons. With x isolated and simplified, we have our solution. Page 21
13) Find y. When solving an equation for a variable, the goal is to get the variable, y, by itself. The first step to isolate y is to multiply both sides of the equation by 5/2. On the left side of the equation, the numbers cancel, leaving y isolated. With y isolated, we can complete the multiplication on the right side of the equation as we have done in previous lessons. With y isolated and simplified, we have our solution. Page 22
14) Find x. When solving an equation for a variable, the goal is to get the variable, x, by itself. To isolate x, we can multiply each side of the equation by 9/4. On the left side of the equation, the 4 s and 9 s cancel, leaving x isolated. On the right side of the equation, since 4 is the same as 4/1, we can cancel a 4 from the top and bottom. We re then left with -9/1, which simplifies to just -9. With x isolated and simplified, we have our solution. Page 23