Solving Simple Algebraic Equations Practice Questions

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Solving Simple Algebraic Equations Practice Questions

Problems

Practice 1

Find the value of the variable in each equation.

1. u + 9 = 17
2. –7s = 49
3. y –13 = 27
4. = 35
5. 54 = 9c
6. h –1 = –1
7. = 6
8. 12 = e + 19
9. –2p = –48
10. = 33
11. 12 + a = 2a
12. 9 – v = 0

Practice 2

Solve for x in terms of y.

1. x + 4 = y – 6
2. 2x = 8y
3. x – 7 = 3y
4. = y + 1
5. 3x = –12y + 15

Solutions

Practice 1

1. In the equation u + 9 = 17, 9 is added to u.

   Use the opposite operation, subtraction, to solve the equation. Subtract 9 from both sides of the equation:  

   u + 9 – 9 = 17 – 9

   u = 8

2. In the equation –7s = 49, s is multiplied by –7. Use the opposite operation, division, to solve the equation. Divide both sides of the equation by –7:

   

   s = –7

3. In the equation y – 13 = 27, 13 is subtracted from y. Use the opposite operation, addition, to solve the equation. Add 13 to both sides of the equation:

   y – 13 + 13 = 27 + 13

   y = 40

4. In the equation = 35, f is divided by 5. Use the opposite operation, multiplication, to solve the equation. Multiply both sides of the equation by 5:

   5 = 5(35)

   f = 175

5. In the equation 54 = 9c, c is multiplied by 9. Use the opposite operation, division, to solve the equation. Divide both sides of the equation by 9:

   

   c = 6

6. In the equation h – 1 = –1, 1 is subtracted from h. Use the opposite operation, addition, to solve the equation. Add 1 to both sides of the equation:

   h – 1 + 1 = –1 + 1

   h = 0

7. In the equation = 6, w is divided by 8. Use the opposite operation, multiplication, to solve the equation. Multiply both sides of the equation by 8:

   8 = 8(6)

   w = 48

8. In the equation 12 = e + 19, 19 is added to e. Use the opposite operation, subtraction, to solve the equation. Subtract 19 from both sides of the equation:

   12 – 19 = e + 19 – 19

   e = –7

9. In the equation –2p = –48, p is multiplied by –2. Use the opposite operation, division, to solve the equation. Divide both sides of the equation by –2:

   

   p = 24

10. In the equation k = 33, k is multiplied by . Use the opposite operation, division, to solve the equation. Divide both sides of the equation by (which is the same as multiplying by the reciprocal ):

    

    k = 44

11. In the equation 12 + a = 2a, a is on both sides of the equal sign. Dividing both sides by 2 will not get a alone on one side of the equation. Subtracting 12 from both sides will not get a alone, either. Instead, subtract a from both sides of the equation:

    12 + a – a = 2a – a

    a = 12

12. In the equation 9 – v = 0, if we subtract 9 from both sides, we will have –v = –9. We are looking to get v, not –v, alone on one side of the equation. Instead, add v to both sides of the equation:

    9 – v + v = 0 + v

    v = 9