Free Printable L2.4 - 2.7 Review

1.

Write the following in interval notation.

x < 8

a)

(8, -∞)

b)

(-∞, 8]

c)

(-∞, 8)

2.

Can you use the symbols [ or ]
with infinity?

a)

Yes

b)

No

3.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

4.

Write the following in interval notation.

x ≥ 100

a)

(0, 100]

b)

(∞, 100]

c)

[100, ∞)

5.

Write this in interval notation.

$x>-9$

a)

$\left(-9,\ \infty\right)$

b)

$\left[-9,\ \infty\right]$

c)

$\left[-9.\ \infty\right)$

6.

Write this in interval notation.

$x\le6$

a)

$\left(-\infty,\ 6\right]$

b)

$\left(-\infty,\ 6\right)$

c)

$\left[-\infty,\ 6\right]$

7.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

8.

Convert this interval notation to inequality notation.

$x\le0$

a)

$\left(-\infty,\infty\right)$

b)

$\left(-\infty,0\right]$

c)

$\left(-\infty,0\right)$

9.

Look at the picture. Which graph best represents the solution set (-∞, -2) U (5, ∞)?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

10.

Look at the picture. Which number line corresponds to [-2, 5]?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

11.

Look at the Graph. Write the inequality in interval notation.

a)

[-4, -1)

b)

(-4, -1)

c)

(-4, -1]

d)

[-4, -1]

12.

Write the following in interval notation

x < 3 or x ≥ 5

a)

(3, -∞) U (∞, 5]

b)

[-∞, 3) U [5, ∞]

c)

(-∞, 3) U [5, ∞)

d)

(3, -∞] U [∞, 5]

e)

(3, -∞] U [5, ∞]

13.

Write the following in interval notation
x < 8

a)

(8, ∞)

b)

(8, -∞)

c)

(-∞, 8)

d)

[-∞, 8]

14.

Write the following in interval notation

-7 ≤ x < 8

a)

(-7, 8)

b)

[-7, 8)

c)

[-7, 8]

d)

(-7, 8]

e)

(8, -7]

15.

Express the following in Interval Notation

-8 ≤ x < 8

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

e)

(8, -8]

16.

Solve and write your answer in interval notation.

a-6\le15+8a

a)

[-3, ∞)

b)

(-∞, -3]

c)

(3, ∞)

d)

(-3, ∞]

17.

Solve and write your answer in interval notation.

28-7x\le-4\left(-7x-7\right)

a)

(0, ∞)

b)

[0, ∞)

c)

(0, ∞]

d)

(-∞, 0]

18.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

d)

(-5, ∞)

19.

Solve the following inequality. Express the solution in interval notation:

5z - 2 < 13 + 2z

a)

(5, ∞)

b)

(-∞, 5)

c)

(1, ∞)

d)

(-∞, 1)

20.

Which is a solution of...

5(v + 3) > 10v - 10

a)

(-∞, 5)

b)

(5, ∞)

c)

(-5, ∞)

d)

(-∞, -5)

21.

Express the following in Interval Notation
-8 ≤ x < 8

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

22.

Express the following in Interval Notation
-9 < x ≤ -4

a)

[-9, -4]

b)

(-9,-4]

c)

[-9, -4]

d)

(-9,-4)

23.

Look at the picture. Which number line corresponds to [-2, 5]?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

24.

Write the following in interval notation

x < 8

a)

[8, ∞)

b)

(8, -∞)

c)

(-∞, 8]

d)

(-∞, 8)

25.

Write the following in interval notation

-7 ≤ x < 8

a)

(-7, 8)

b)

[-7, 8)

c)

[-7, 8]

d)

(-7, 8]

26.

Write the inequality in interval notation.

a)

[-4, -1)

b)

(-4, -1)

c)

(-4, -1]

d)

[-4, -1]

27.

Solve and write your answer in interval notation.

a-6\le15+8a

a)

[-3, ∞)

b)

(-∞, -3]

c)

(3, ∞)

d)

(-3, ∞]

28.

Solve and write your answer in interval notation.

28-7x\le-4\left(-7x-7\right)

a)

(0, ∞)

b)

[0, ∞)

c)

(0, ∞]

d)

(-∞, 0]

29.

Express the following in Interval Notation

-8 ≤ x < 8

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

30.

Express the following interval as an inequality:

[3, 5]

a)

3 ≤ x ≤ 5

b)

3 < x ≤ 5

c)

3 ≤ x < 5

d)

3 < x < 5

31.

Express the following interval as an inequality:

(-7, 15]

a)

-7 ≤ x ≤ 15

b)

-7 < x ≤ 15

c)

-7 ≤ x < 15

d)

-7 < x < 15

32.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

d)

(-5, ∞)

33.

Solve the following inequality. Express the solution in interval notation:

5z - 2 < 13 + 2z

a)

(5, ∞)

b)

(-∞, 5)

c)

(1, ∞)

d)

(-∞, 1)

34.

Which is a solution of...

5(v + 3) > 10v - 10

a)

(-∞, 5)

b)

(5, ∞)

c)

(-5, ∞)

d)

(-∞, -5)

35.

Solve the following inequality:
$5-\left(4x-5\right)\le30$

a)

x ≤ -5

b)

x < 10

c)

x ≥ -5

d)

x ≥ 10

36.

Solve

-2x+3\left(-4x+6\right)\le116

a)

x ≤ -7

b)

x ≥ 29

c)

x ≥ -7

d)

x ≤ 29

37.

Solve 5( 6 + 3r) + 7 ≥ 127. Express the solution in interval notation.

a)

(-∞, 6]

b)

[6, ∞)

c)

(-∞, -6]

d)

[-6, ∞)

38.

Solve the following inequality. Express the solution in interval notation:

-3\le2x-1\le5

a)

[-1, 3]

b)

(-1, 3)

c)

(1, 3)

d)

[1, 3]

39.

a)

x > 7.25

b)

x < 11.5

c)

x >13.5

d)

x < 12.5

40.

Solve: -3 ≤ 2x - 1 ≤ 5

a)

-1 ≤ x ≤ 3

b)

-1 < x < 3

c)

1 < x < 3

d)

1 ≤ x ≤ 3

41.

\left|6m\right|=42

a)

{7,-7}

b)

{6,-6}

c)

{6,0}

d)

{-7,6}

42.

$\left|-6x\right|=30$

a)

{4,-4}

b)

{5,0}

c)

{-5,5}

d)

{3,-10}

43.

$\left|k-10\right|=3$

a)

{-3,10}

b)

{10,-10}

c)

{-7,-13}

d)

{13,7}

44.

$\left|\frac{x}{7}\right|=3$

a)

{21,-21}

b)

{4,-4}

c)

{10,-10}

d)

{10,-4}

45.

\left|7+p\right|=7

a)

{0,-1}

b)

{0,-14}

c)

{0,0}

d)

{1,-1}

46.

$\left|-3p\right|=15$

a)

{12,5}

b)

{-5,18}

c)

{18,12}

d)

{-5,5}

47.

$7\left|n\right|=56$

a)

{-8,0}

b)

{49,53}

c)

{8,-8}

d)

{49,14}

48.

$\frac{\left|m\right|}{5}=3$

a)

{15,-15}

b)

$\left\{\frac{3}{5},-\frac{3}{5}\right\}$

c)

{2,-2}

d)

{8,-8}

49.

$\left|n\right|+1=2$

a)

{2,-2}

b)

{3,-3}

c)

{1,-1}

d)

{1,2}

50.

$\frac{\left|a-5\right|}{8}=5$

a)

{45,-35}

b)

{48,34}

c)

{80,0}

d)

{36,47}

51.

$\left|\frac{x}{7}\right|-8=-7$

a)

{-57,-41}

b)

{15,-1}

c)

{8,-8}

d)

{7,-7}

52.

$4\left|n+8\right|=56$

a)

{14,16}

b)

{6,-22}

c)

$\left\{\frac{51}{8},\frac{-51}{8}\right\}$

d)

{-8,8}

53.

$\frac{\left|-9+v\right|}{8}=3$

a)

{24,-24}

b)

{30,18}

c)

{33,-15}

d)

{27,21}

54.

$-10\left|v+2\right|=-70$

a)

{5,-9}

b)

{7,-7}

c)

{50,90}

d)

{9,-5}

55.

$\left|5x\right|+5=45$

a)

{14,4}

b)

{40,35}

c)

{8,-8}

d)

{45,-45}

56.

$-5\left|3+4k\right|=-115$

a)

$\left\{5,\frac{-13}{2}\right\}$

b)

{5,-5}

c)

{-13,13}

d)

{13,2}

57.

\frac{\left|7p+4\right|}{8}=3

a)

{20,4}

b)

$\left\{\frac{20}{7},-4\right\}$

c)

$\left\{\frac{7}{20},10\right\}$

d)

{7,-4}

58.

$2-5\left|5m-5\right|=-73$

a)

{4,-2}

b)

{6,-8}

c)

{2,-4}

d)

{4,-1}

59.

$6\left|1-5x\right|-9=57$

a)

{-2,5}

b)

$\left\{-2,\frac{12}{5}\right\}$

c)

{2,-12}

d)

$\left\{2,\frac{-15}{4}\right\}$

60.

$3\left|3-5r\right|-3=18$

a)

$\left\{\frac{-4}{5},2\right\}$

b)

{2,4}

c)

{-4,5}

d)

$\left\{\frac{4}{3},-1\right\}$

61.

$\left|x\right|\ge5$

a)

$-5\le x\le5$

b)

$x\ge5\ or\ x\le-5$

c)

5,-5

d)

25

62.

$\left|2x\right|\le10$

a)

$-5\le x\le5$

b)

$x\ge5\ or\ x\le-5$

c)

5,-5

d)

25

63.

$\left|x\right|\le2$

a)

$-2\le x\le2$

b)

$x\ge2\ or\ x\le-2$

c)

2,-2

d)

4

64.

$\left|x\right|\ge12$

a)

0

b)

$-12\le x\le12$

c)

$x\ge12\ or\ x\le-12$

d)

12,-12

65.

$\left|3x\right|\ge12$

a)

4,9

b)

$x\ge4\ or\ x\le-4$

c)

$x\ge9\ or\ x\le-9$

d)

$-4\le x\le4$

66.

$\left|x+1\right|<6$

a)

-7 < x < 5

b)

-7

c)

-6 < x < 6

d)

-5 < x < 7

67.

$\left|5x\right|\ge25$

a)

$x>5\ or\ x<-5$

b)

$-5\le x\le5$

c)

x < 25

d)

5,-5

68.

$\left|3x\right|>24$

a)

$x<8\ or\ x>-8$

b)

8,-8

c)

$x>8\ or\ x<-8$

d)

72,-72

69.

$\left|2x+1\right|>7$

a)

$-5<x\le3$

b)

$x>3\ or\ x<-4$

c)

-5, -3

d)

$-4\le x\le3$

70.

$\left|\frac{x}{5}\right|<10$

a)

$x\le50\ or\ x\ge-50$

b)

$x>5\ or\ x<-5$

c)

$-2<x<2$

d)

$-50<x<50$

71.

Solve:
|x + 3| > 8

a)

x > 5 or x < -11

b)

x > 5

c)

all real numbers

d)

no solution

72.

Solve:
|x + 3| > - 8

a)

x > 5 or x < -11

b)

x > 5

c)

all real numbers

d)

no solution

73.

Solve:
3 | 2x + 7| - 7 < -4

a)

x < -3 and x > -5/3

b)

x < -3 and x > -4

c)

all real numbers

d)

no solution

74.

Solve:
3 | 2x + 7| + 7 < 4

a)

x < -3 and x > -5/3

b)

x < -3 and x > -4

c)

all real numbers

d)

no solution

75.

Solve:
|x + 4| + 8 > 2

a)

x < -3 and x > -5/3

b)

x < -3 and x > -4

c)

all real numbers

d)

no solution

76.

Solve:
|x + 4| - 8 > 2

a)

x > 6 and x < 10

b)

x > 6 or x < -14

c)

all real numbers

d)

no solution

77.

Solve.
|2x - 1| = 7

a)

x = -3 or x = 4

b)

x = 4

c)

x = 4 or x = -4

d)

no solution

78.

Solve.
|2x - 1| = -7

a)

x = -3 or x = 4

b)

all real numbers

c)

x = 3 or x = -3

d)

no solution

79.

Solve.
|2x - 12| + 8 = 8

a)

x = 6 or x = -2

b)

x = 6 or x = -6

c)

no solution

d)

x = 6

80.

Solve.
-5|x - 4| > -20

a)

x < 8 and x > 0

b)

x > 8 or x < 0

c)

all real numbers

d)

no solution

81.

Solve.
-5|x - 4| > 20

a)

x < 8 and x > 0

b)

x > 8 or x < 0

c)

all real numbers

d)

no solution

82.

Solve.
-5|x - 4| < 20

a)

x < 8 and x > 0

b)

x > 8 or x < 0

c)

all real numbers

d)

no solution

L2.4 - 2.7 Review

Total questions: 82

Worksheet time: 7hrs 50mins

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