# Solving Equations Exercises Set 1A Answers

Below are the answers to Solving Equations Exercises Set 1A.

Part I

1. $x + 2 = 10$
$x = 10 - 2$
$x = 8$

2. $x - 7 = -14$
$x = -14 + 7$
$x = -7$

3. $4x = 20$
$x = \frac{20}{4}$
$x = 5$

4. $-3x = 18$
$x = \frac{18}{-3}$
$x = -6$

5. $\frac {x}{4} = 20$
$x = 20(4)$
$x = 80$

6. $\frac {x}{9} = -10$
$x = -10(9)$
$x = -90$

7. $2x + 1 = 15$
$2x = 15 - 1$
$2x = 14$
$x = \frac {14}{2}$
$x = 7$

8. $4x - 7 = 13$
$4x = 13 + 7$
$4x = 20$
$x = \frac {20}{4}$
$x = 5$

9. $-6x + 2 = -14$
$-6x = -14 - 2$
$-6x = -16$
$x = \frac {-16}{-6}$
$x = \frac {8}{3}$ or $2 \frac {2}{3}$

10. $3x - 1 = 8$
$3x = 8 + 1$
$3x = 9$
$x = \frac {9}{3}$
$x = 3$

Part II

1. $9 - x = 17$
$-x = 17 - 9$
$-x = 12$
$x = \frac {12}{(-1)}$
$x = -12$

2. $4x - 7 = -15$
$4x = -15 + 7$
$4x = -8$
$x = \frac {-8}{4}$
$x = -2$

3. $7x + 36 = 4x$
$7x - 4x = -36$
$3x = -36$
$x = \frac {-36}{3}$
$x = -12$

4. $-2x - 11 = -x$
$-2x + x = 11$
$-x = 11$
$x = \frac {11}{-1}$
$x = -11$

5. $7x = 5x - 6$
$7x - 5x = -6$
$2x = -6$
$x = \frac {-6}{2}$
$x = -3$

6. $2x - 5 = x + 4$
$2x -x = 4 + 5$
$x = 9$

7. $9x + 6 = 7x - 8$
$9x - 7x = -8 - 6$
$2x = -14$
$x = \frac {-14}{2}$
$x = -7$

8. $9 - x = 2 + 6x$
$-x - 6x = 2 - 9$
$-7x = -7$
$x = \frac {-7}{-7}$
$x = 1$

9. $\frac {x}{2} = x + 7$
$x = 2(x + 7)$
$x = 2x + 14$
$x - 2x = 14$
$-x = 14$
$x = \frac {14}{-1}$
$x = -14$

10. $-\frac {1}{4}x = 3x - 12$
$-x = 4(3x - 12)$
$-x = 12x - 48$
$-x - 12x = - 48$
$-13x = -48$
$x = \frac {-48}{-13}$
$x = \frac {48}{13}$ or $3 \frac {9}{13}$

Part III

1. $2(x - 5) = -8$
$2x - 10 = -8$
$2x = -8 + 10$
$2x = 2$
$x = 1$

2. $6(2x - 1) = -8 + x$
$12x - 6 = -8 + x$
$12x - x = -8 + 6$
$11x = -2$
$x = \frac {-2}{11}$

3. $3(4 - 3x) = 3x$
$12 - 9x = 3x$
$-9x - 3x = -12$
$-12x = -12$
$x = 1$

4. $5(x- 7) - 2 = x - 1$
$5x - 35 - 2 = x - 1$
$5x - 37 = x - 1$
$5x - x = -1 + 37$
$4x = 36$
$x = \frac {36}{4}$
$x = 9$

5. $4(x - 1) = 3(x + 1)$
$4x - 4 = 3x + 3$
$4x - 3x = 3 + 4$
$x = 7$

6. $7(4 - 2x) = x - 2$
$28 - 14x = x - 2$
$-14x - x = -2 - 28$
$-15x = -30$
$x = \frac {-30}{-15}$
$x = 2$

7. $4 - 6(x - 7) = -x - 4$
$4 - 6x + 42 = -x - 4$
$-6x + 48 = -x - 4$
$-6x + x = -4 - 48$
$-5x = -52$
$x = \frac {-52}{-5}$
$x = \frac {52}{5}$ or $10 \frac {2}{5}$

8. $\frac {-x}{4} = x + 10$
$-x = 4(x + 10)$
$-x = 4x + 40$
$-x - 4x = 40$
$-5x = 40$
$x = \frac {40}{-5}$
$x = -8$

9. $3x + \frac {1}{2} = 12$
To eliminate the fractions, we multiply both sides by 2.

$2(3x + \frac {1}{2}) = 2(12)$
$6x + 1 = 24$
$6x = 24 - 1$
$6x = 23$
$x = \frac {23}{6} or 3 \frac {5}{23}$

10. $\frac {3x}{5} = 4x - 8$
$3x = 5(4x - 8)$
$3x = 20x - 40$
$3x - 20x = -40$
$-17x = -40$
$x = \frac {-40}{-17}$
$x = \frac {40}{17}$ or $x = 2 \frac {6}{17}$

We will have more exercises soon.

### 3 Responses

1. OMS says:

Part 2 number 1 is wrong. 17 minus 9 is 8 not 12

2. OMS says:

The solution for Part 2 number 7 is incorrect. Kindly analyze it.

3. OMS says:

Part 3 number 7 rather.