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.

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