Integers and equations

Adding and subtracting integers, multiplying and dividing them, one- and two-step equations, inequalities and proportionality.

7 sheets · 56 questions · one answer key · 8 pages

Recommended for grades 6–7

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Integers Sheet 1 of 7

Integers, add and subtractWithin 20

Name: Date:

Add or subtract the integers.

1−14 + 8 =

27 − 13 =

3−1 + 11 =

40 − 17 =

54 − 11 =

6−11 + 17 =

7−6 + 3 =

87 − 9 =

Integers, multiply and divideFactors to 12

Name: Date:

Multiply or divide. Remember what two negative signs make.

1−18 ÷ (−3) =

2−11 × (−8) =

399 ÷ (−9) =

4−48 ÷ (−12) =

511 × (−2) =

6−2 × (−5) =

710 × (−7) =

8−54 ÷ (−6) =

Solving equationsTo 50

Name: Date:

Solve each equation for x.

1x + 41 = 49

2x + 11 = 36

3x − 5 = 34

423 − x = 20

529 − x = 28

6x + 8 = 37

7x − 14 = 35

8x + 8 = 20

Solving equationsTo 50

Name: Date:

Solve each equation for x.

12x = 18

22x = 20

3x ÷ 3 = 13

42x = 50

5x ÷ 2 = 10

6x ÷ 10 = 4

7x ÷ 2 = 14

87x = 35

Solving equationsTo 50

Name: Date:

Solve each equation for x.

17x − 27 = 8

22x − 8 = 20

37x + 10 = 17

44x + 8 = 36

57x + 1 = 15

62x + 1 = 31

74x − 2 = 22

82x − 38 = 10

InequalitiesTo 50

Name: Date:

Solve each one, then write >, <, ≥ or ≤ in the box.

1x + 5 ≤ 31x26

2x + 12 ≤ 18x6

3x + 9 ≤ 13x4

4x + 6 ≤ 41x35

5x + 7 > 17x10

6x + 8 > 25x17

7x − 9 ≤ 15x24

8x − 5 > 26x31

Constant of proportionalityThe constant of proportionality

Name: Date:

Find the constant of proportionality for each table.

1x3589y6101618k

2x3679y27546381k

3x3689y367296108k

4x2789y6212427k

5x4578y16202832k

6x4578y44557788k

7x2689y6182427k

8x2468y20406080k

Power Pack · Integers and equationsAnswer key

Integers

1. -14 + 8 = -62. 7 − 13 = -63. -1 + 11 = 104. 0 − 17 = -175. 4 − 11 = -76. -11 + 17 = 67. -6 + 3 = -38. 7 − 9 = -2

Integer × ÷

1. -18 ÷ -3 = 62. -11 × -8 = 883. 99 ÷ -9 = -114. -48 ÷ -12 = 45. 11 × -2 = -226. -2 × -5 = 107. 10 × -7 = -708. -54 ÷ -6 = 9

One-step: + and −

1. x + 41 = 49 → x = 82. x + 11 = 36 → x = 253. x − 5 = 34 → x = 394. 23 − x = 20 → x = 35. 29 − x = 28 → x = 16. x + 8 = 37 → x = 297. x − 14 = 35 → x = 498. x + 8 = 20 → x = 12

One-step: × and ÷

1. 2x = 18 → x = 92. 2x = 20 → x = 103. x ÷ 3 = 13 → x = 394. 2x = 50 → x = 255. x ÷ 2 = 10 → x = 206. x ÷ 10 = 4 → x = 407. x ÷ 2 = 14 → x = 288. 7x = 35 → x = 5

Two-step equations

1. 7x − 27 = 8 → x = 52. 2x − 8 = 20 → x = 143. 7x + 10 = 17 → x = 14. 4x + 8 = 36 → x = 75. 7x + 1 = 15 → x = 26. 2x + 1 = 31 → x = 157. 4x − 2 = 22 → x = 68. 2x − 38 = 10 → x = 24

Inequalities

1. x + 5 ≤ 31 → x ≤ 262. x + 12 ≤ 18 → x ≤ 63. x + 9 ≤ 13 → x ≤ 44. x + 6 ≤ 41 → x ≤ 355. x + 7 > 17 → x > 106. x + 8 > 25 → x > 177. x − 9 ≤ 15 → x ≤ 248. x − 5 > 26 → x > 31

Proportionality

1. x: 3, 5, 8, 9 y: 6, 10, 16, 18 → k = 22. x: 3, 6, 7, 9 y: 27, 54, 63, 81 → k = 93. x: 3, 6, 8, 9 y: 36, 72, 96, 108 → k = 124. x: 2, 7, 8, 9 y: 6, 21, 24, 27 → k = 35. x: 4, 5, 7, 8 y: 16, 20, 28, 32 → k = 46. x: 4, 5, 7, 8 y: 44, 55, 77, 88 → k = 117. x: 2, 6, 8, 9 y: 6, 18, 24, 27 → k = 38. x: 2, 4, 6, 8 y: 20, 40, 60, 80 → k = 10

Integers and equations

What is in the pack

The algebra track

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