## 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.

## PEMDAS Exercises Set 1 Answers

Below are the answers to PEMDAS Exercises Set 1.

Part I

1. $5 + 3 - 2$
$= 8 - 2$
$= 6$

2. $9 - 6 + 4$
$= 3 + 4$
$= 7$

Note: Be careful! A lot of people make mistakes in number 2. If no other operation is between addition and subtraction, you operate from left to right. Here, we must subtract first before we add.

3. $7 + 4 \times 3$
$= 7 + 12$
$= 19$

4. $6 \times (-2) + 3$
$= -12 + 3$
$= -9$

5. $2 \times (-9 + 4)$
$= 2 \times (-5)$
$= -10$

6. $60 \div (-6 + 2)$
$= 60 \div (-4)$
$= -15$

7. $(-3 - 11) \times (-7)$
$= (-14) \times (-7)$
$= 98$

8. $12 \div 3 \times 5$
$= 4 \times 5$
$= 20$

Note: Be careful! Just like in number 2, if no other operation is between multiplication and division, you operate from left to right. Here, we must divide first before we multiply.

9. $4 \times (-1 - 6)$
$= 4 \times (-7)$
$= -28$

10. $-5 + (13 - 7) \div 3$
$= -5 + (6) \div 3$
$= -5 + 2$
$= -3$

Part II
1. $4 \times (-3 - 5)$
$= 4 \times (-8)$
$= -32$

2. $-2 \times (3 + 6)$
$= -2 \times (9)$
$= -18$

3. $(9 - 13) \div (-1)$
$= (-4) \div (-1)$
$= 4$

4. $(4 + 6)^2 - 7$
$= (10)^2 - 7$
$= (100) - 7$
$= 93$

5. $(-4)^2 \times (-2)^3$
$= (16) \times (-8)$
$= -128$

6. $-3 - 7 \times 2$
$= -3 - 14$
$= -17$

7. $= 3 - (-2) + 8$
$= 3 + 2 + 8$
$= 13$

8. $-12 - 8 \div 4$
$= -12 - 2$
$= -14$

9. $9 - (-4^2) \times (-2)$
$= 9 - (-16) \times (-2)$
$= 9 - 32$
$= -23$

Note the difference: $latex -4^2 = -16$ and $(-4)^2 = 16$.

10. $10 \div (-2) - (-3 \times 4)$
$= 10 \div (-2) - (-3 \times 4)$
$= (-5) - (-12)$
$= -5 + 12$
$= 7$

Part III
1. $3 - (-2) \times 5$
$= 3 - (-10)$
$= 3 + 10$
$= 13$

2. $-4 \times 3 + 6 \times 2$
$= -12 + 12$
$= 0$

3. $16 \div (-2) + 12 \div 4$
$= -8 + 3$
$= -5$

4. $36 \div (-13 + 4)$
$= 36 \div (-9)$
$= -4$

5. $18 \div (-3)^2 + (-4)$
$= 18 \div (9) + (-4)$
$= 2 + (-4)$
$= -2$

6. $4 \times (-2) + (-3^2)$
$= 4 \times (-2) + (-9)$
$(-8) + (-9)$
$= -17$

Note: Be careful! Please note that $-3^2 = -9$ and  $(-3)^2 = 9$.

7. $3 \times [-4 - (12 - 5)]$
$= 3 \times [-4 - (7)]$
$= 3 \times [-11]$
$= -33$

8. $(-3)^2 + 2^3 \div (-4)$
$= 9 + 8 \div (-4)$
$= 9 + (-2)$
$= 7$

9. $9 - (-4^2) \times (-2)$
$= 9 - 16 \times (-2)$
$= 9 - (32)$
$= -23$

Note: Again, $-4^2) = -16$, not $16$.

10. $-2 \times (-3 \times 2)^2 - (-2)^2$
$= -2 \times (-6)^2 - (4)$
$= -2 \times (36) - (4)$
$= -72 - (4)$
$= -76$

## Division of Integers Exercises Set 1 Answers

Below are the answers to Division of Integers Exercises (Set 1).
Part I

1. -4

2. -4

3. 7

4. -5

5. 0

6. 18

7. -5

8. -2

9. 2

10. 6

Part II

1. -2

2. -5

3. 7

4. -7

5. 0

6. 6

7. -9

8. -5

9. 1

10. -9

Part III

1. $\frac {1}{2} \div (-\frac {1}{4}) = \frac {1}{2} \times (-\frac {4}{1}) = \frac {4}{2} = -2$

2. $-\frac {2}{5} \div (-\frac {3}{4}) = -\frac {2}{5} \times (-\frac {4}{3}) = \frac {8}{15}$

3. $-\frac {3}{4} \div \frac {3}{8} = -\frac {3}{4} \times \frac {8}{3} = (-\frac {24}{12}) = -2$

4. $\frac {4}{5} \div (-\frac {1}{5}) = \frac {4}{5} \times (-\frac {5}{1}) = -\frac {20}{5} = -4$

5. $-\frac {5}{7} \div \frac {1}{2} = -\frac {5}{7} \times \frac {2}{1} = -\frac {10}{7} = -1 \frac {3}{7}$

6. -2

7. 3

8. -5

9. -4

10. 0

Now, that you have compelted the four fundamental operations, you might want to learn about the PEMDAS Rules and answer PEMDAS exercises.

## Multiplication of Integers Exercises Set 1 Answers

Below are the answers to Multiplication of Integers Exercises (Set 1).

Part I

1. -6

2. 28

3. -27

4. 49

5. -33

6. -48

7. 18

8. 0

9. -15

10. 39

Part II

1. -24

2. -32

3. 36

4. 60

5. 0

6. 12

7. -120

8. -21

9. -88

10. 42

Part III

1. $-\frac {1}{6}$

2. $\frac {1}{8}$.

3. $-\frac {1}{8}$

4. $\frac {1}{14}$

5. $-\frac {4}{11}$

6. -1.5

7. -0.08

8. 0.3

9. 0.24

10. 0

## Subtraction of Integers Exercises Set 1 Answers

Below are the answers to Subtraction of Integers Exercises (Set 1).

Part I

1.) 8 – (-7) = 8 + (7) = 15

2.) -4 – (-10) = -4 + (10) = 6

3. -6 – 8 = -6 + (-8) = -14

4. 0 – (-5) = 0 + (5) = 5

5. -17 – (-13) = -17 + (13) = -4

6. 0 – 18 = 0 + (-18) =-18

7. 12 – 19 = 12 + (-19) = -7

8. -11 – 18 = -11 + (-18) = -29

9. 21 – (-22) = 21 + (22) = 43

10. -14 – (-14) = -14 + (14) = 0

Part II

1. 31 – (-14) = 31 + (14) = 45

2. -17 – (-11) = -17 + (11) =-6

3. -19 – 12 = -19 + (-12) = -31

4. 0 – (-17) = 0 + (17) = 17

5. -34 – (-21) = -34 + (21) = -13

6. 0 + (-47) = -47

7. 36 – 42 = 36 + (-42) = -6

8. -25 – 35 = -25 + (-35) = -60

9. 28 – (-30) = 28 + (30) = 58

10. -45 – (-45) = -45 + (45) = 0

Part III

1. $\frac {1}{7} - (-\frac {3}{7}) = \frac {1}{7} + (\frac {3}{7}) = \frac {4}{7}$

2. $-\frac {3}{5} - (-\frac {4}{5}) = -\frac {3}{5} + (\frac {4}{5})= \frac {1}{5}$

3. $-\frac {3}{4} - \frac {1}{4} = -\frac {3}{4} +(-\frac {1}{4}) = -\frac {4}{4} = -1$

4. $\frac {7}{11} - \frac {9}{11} = \frac {7}{11} + (-\frac {9}{11}) = -\frac {2}{11}$

5. $-\frac {5}{12} - (-\frac {5}{12}) = -\frac {5}{12} + (\frac {5}{12}) = 0$

6. 0.4 – (-0.3) = 0.4 + (0.3) = 0.7

7. -0.8 – (-0.7) = -0.8 + (0.7) = -0.1

8. -1.2 – 0.4 = -1.2 + (-0.4) = -1.6

9. 0.3 – 0.9 = 0.3 + (-0.9) = -0.6

10. -0.6 – (-0.6) = -0.6 + (0.6) = 0

1. 6
2. -17
3. -13
4. -4
5. 0
6. -25
7. 23
8. -26
9. 0
10. 34

Part II
1. 10
2. -6
3. 8
4. 0
5. -9
6. -3
7. -6
8. 11
9. 0
10. 11

Part III
1. -2/2 or -1
2. -1/4
3. 0
4. 1/4
5. -7/11
6. 0.4
7. 3.6
8. -1.5
9. 1.5
10. -1.45

You might also want to answer the exercises on subtraction of integers.

## PCSR Civil Service Exam Review Guide 7

PCSR 2017 CIVIL SERVICE EXAM REVIEW GUIDE 7
Updated: May 20, 2017

PART I: MATHEMATICS

A.1 Videos

A.2 More video tutorials

A.3 Articles

PART II: ENGLISH

A. Vocabulary

Civil Service Exam Vocabulary Review Part 7
Tip: Try to memorize the words and use it in your own words.

B. Spelling

Civil Service Exam Spelling Quiz 7

Enjoy!

## Solving Equations Exercises – Set 1A

Below are exercises on solving equations.

Part I

1. $x + 2 = 10$

2. $x - 7 = -14$

3. $4x = 20$

4. $-3x = 18$

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

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

7. $2x + 1 = 15$

8. $4x - 7 = 13$

9. $-6x + 2 = -14$

10. $3x - 1 = 8$

Part II

1. $9 - x = 17$

2. $4x - 7 = -15$

3. $7x + 36 = 4x$

4. $-2x - 11 = -x$

5. $7x = 5x - 6$

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

7. $9x + 6 = 7x - 8$

8. $9 - x = 2 + 6x$

9. $\frac {x}{2} = x + 7$

10. $-\frac {1}{4}x = 3x - 12$

Part III

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

2. $6(2x - 1) = -8 + x$

3. $3(4 - 3x) = 3x$

4. $5(x- 7) - 2 = x - 1$

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

6. $7(4 - 2x) = x - 2$

7. $4 - 6(x - 7) = -x - 4$

8. $-\frac {x}{4} = x + 10$

9. $3x + \frac {1}{2} = 12$

10. $\frac {3x}{5} = 4x - 8$

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