Free Printable Solving and Graphing Linear and Absolute Value Inequalities

1.

| x + 3 | ≤ 2

a)

No Solution

b)

All Real Numbers

c)

-5 ≤ x ≤ -1

d)

1 ≤ x ≤ 5

2.

−2|−2r − 4| = -12

a)

$x=5$ or $x=1$

b)

$x=-5$ or $x=-1$

c)

$x=-5$ or $x=1$

d)

No Solution

3.

Solve:

$\left|12+w\right|\ge-5$

a)

no solution

b)

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

c)

$\left(-\infty,-17\right]\cup\left[-7,\infty\right]$

d)

$\left[-17,-7\right]$

4.

Solve:

$\left|2x+1\right|<-1$

a)

no solution

b)

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

c)

$\left(3,4\right)$

d)

$\left(-\infty,3\right)\cup\left(4,\infty\right)$

5.

$\left|2x-3\right|+5=12$

a)

$x=-2\$

b)

$x=5$

c)

$x=-2$ or $x=5$

d)

$\left[-2,5\right]$

6.

$x>-3\$ and $x>10$ simplifies to which of the following statements.

a)

$x>-3$

b)

$x>10$

c)

$3<x<10$

d)

all real numbers

7.

$x\ge-5$ or $x>7$ simplifies to which of the following?

a)

$x>7$

b)

$-5<x<7$

c)

$x\ge-5$

d)

no solution

8.

$x<-2\$ or $-6\le x$ simplifies to which of the following?

a)

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

b)

no solution

c)

$\left[-6,\ 2\right)$

d)

$\left(-\infty,\ -2\right)$

9.

Solve: $-15\le5-\frac{5}{3}x<10$

a)

$-3<x\le12$

b)

$x\ge12\$ or $x<3$

c)

$-2<x\le10$

d)

$x\le10$ or $x>2$

10.

Solve: $9-2x\le x+3<5x+7$

a)

$\left(-1,\infty\right)$

b)

$\left[2,\infty\right)$

c)

$\left(-1,2\right]$

d)

$\left(-\infty,-1\right)U\left[2,\infty\right)$

11.

Solve: |x + 3| < 8

a)

x > 5 or x < -11

b)

-11 < x < 5

c)

x > 11 or x < -5

d)

5 < x < 11

12.

Solve:
|x + 3| > 8

a)

x > 5 or x < -11

b)

-11 < x < 5

c)

x > 11 or x < -5

d)

-5 < x < 11

13.

Solve: |x - 3| < 8

a)

x > 5 or x < -11

b)

-11 < x < 5

c)

x > 11 or x < -5

d)

-5 < x < 11

14.

Solve: |x - 3| > 8

a)

x > 5 or x < -11

b)

-11 < x < 5

c)

x > 11 or x < -5

d)

-5 < x < 11

15.

Solve: |2x + 1| ≤ 19

a)

x ≥ 9 or x ≤ -10

b)

-10 ≤ x ≤ 9

c)

x ≥ 10 or x ≤ -9

d)

-9 ≤ x ≤ 10

16.

Solve: |2x - 1| ≥ 19

a)

x ≥ 9 or x ≤ -10

b)

-10 ≤ x ≤ 9

c)

x ≥ 10 or x ≤ -9

d)

-9 ≤ x ≤ 10

17.

Solve: |2x - 1| ≤ 19

a)

x ≥ 9 or x ≤ -10

b)

-10 ≤ x ≤ 9

c)

x ≥ 10 or x ≤ -9

d)

-9 ≤ x ≤ 10

18.

Solve: |2x + 1| ≥ 19

a)

x ≥ 9 or x ≤ -10

b)

-10 ≤ x ≤ 9

c)

x ≥ 10 or x ≤ -9

d)

-9 ≤ x ≤ 10

19.

Solve: |k| < 8

a)

x > 8 or x < -8

b)

-8 < k < 8

c)

No solution

d)

Infinite solution

20.

Solve: |k| > 8

a)

x > 8 or x < -8

b)

-8 < k < 8

c)

No solution

d)

Infinite solution

21.

Solve: |k| > -8

a)

x > 8 or x < -8

b)

-8 < k < 8

c)

No solution

d)

Infinite solution

22.

Solve: |k| < -8

a)

x > 8 or x < -8

b)

-8 < k < 8

c)

No solution

d)

Infinite solution

23.

Solve.

a)

-1 < r or r < 9

b)

-1 < r < 9

c)

r < 9

d)

-1 < r

24.

Solve.

a)

b < -8

b)

b > -8

c)

All real numbers

d)

No solution

25.

Solve.

a)

no solution

b)

-6 ≤ r ≥ 8

c)

6 > r > -8

d)

-6 < r < 8

26.

Graph after solving: $-3x+5\ge8$

a)

b)

c)

d)

27.

Graph after solving: $-2x+15<19$

a)

b)

c)

d)

28.

Graph after solving: $4\left(x-12\right)>-24$

a)

b)

c)

d)

29.

Graph after solving: $-3\left(2x-5\right)\ge27$

a)

b)

c)

d)

30.

Graph after solving: $7\left(2x+1\right)-3\left(x-1\right)\le43$

a)

b)

c)

Set of all Reals

d)

31.

Graph after solving: $5\left(x+2\right)-15<15x-25$

a)

b)

c)

d)

32.

Graph after solving: $2\left(x-4\right)+4x>3\left(2x+5\right)$

a)

Set of all Reals

b)

No solution

c)

d)

33.

Graph after solving: $-5x+\left(x-3\right)\le-4\left(x-2\right)$

a)

Set of all Reals

b)

No solution

c)

d)

34.

Graph after solving: $-\frac{1}{2}x+7>5$

a)

b)

c)

d)

35.

Graph after solving: $\frac{-4x+10}{3}\le6$

a)

b)

c)

d)

36.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

37.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

38.

c - 7 > 8

a)

c < 15

b)

c > 15

c)

c < - 15

d)

c >, = 15

39.

Solve
y - 4 > 12

a)

y > 16

b)

y < 16

c)

y > 8

d)

y < 8

40.

What inequality does the number line graph represent?

a)

x ≤ 4

b)

x ≥ -4

c)

x < -4

d)

x < 4

41.

The sign below means...
≥

a)

Greater Than

b)

Less Than

c)

Greater Than or Equal to

d)

Less Than or Equal to

42.

<

a)

equal

b)

less than

c)

less than or equal to

d)

at least

43.

≤

a)

equal

b)

less than

c)

less than or equal to

d)

at least

44.

≥

a)

equal

b)

greater than

c)

greater than or equal to

d)

at most

45.

>

a)

equal

b)

greater than

c)

greater than or equal to

d)

at most

46.

m - 5 > 10

a)

m is less than 15

b)

m is greater than 5

c)

m is greater than 15

d)

m is less than 5

47.

If you were to graph x > 2, what would you do?

a)

put a closed dot on 2 and to the right

b)

put a closed dot on 2 and to the left

c)

put an open dot on 2 and to the right

d)

put an open dot on 2 and to the left

48.

What do you do to solve the graph of the inequality:
-2x ≤ 10

a)

divide by -2

b)

multiply by -2

c)

multiply by -2 and flip the inequality

d)

divide by -2 and flip the inequality

49.

Which is the solution of
-6a ≥ -36

a)

a ≥ 6

b)

-6 ≥ a

c)

a ≤ 6

d)

6 ≤ a

50.

How many answers are there in an inequality?

a)

0

b)

1

c)

2

d)

multiple

51.

Which of the following inequalities would require you to flip the sign when solving?

a)

2x < 3

b)

3x > - 9

c)

-4x ≥ 10

d)

5x ≤ 15

52.

What does the inequality sign mean?

a)

greater than

b)

less than

c)

greater than or equal to

d)

less than or equal to

53.

What does the inequality sign mean?

a)

greater than

b)

less than

c)

greater than or equal to

d)

less than or equal to

54.

How can I tell if an inequality will have a solid line?

a)

It has an equal sign.

b)

The symbol is greater than.

c)

The symbol has "or equal to."

d)

You just guess.

55.

When graphing an inequality, you use a dotted line when you use which symbol?

a)

<, >

b)

≤, ≥

56.

Consider the function y<2x+3. Which is true?

a)

The line would be solid with shading above.

b)

The line would be dashed with shading above.

c)

The line would be solid with shading below.

d)

None of these.

57.

Which of the following equations match the given graph?

a)

y ≥ 2/5x + 1

b)

y ≥ -2/5x + 1

c)

y≤ 2/5x + 1

d)

y ≥ -2/5x - 1

58.

Which of the following inequalities matches the graph?

a)

y ≤ 3/4x + 5

b)

y ≥ 3/4x + 5

c)

y < 3/4x + 5

d)

y > 3/4x + 5

59.

Which of the following equations match the given graph?

a)

y ≤ -3/4 x + 3

b)

y ≥ -3/4 x + 3

c)

y < -3/4 x + 3

d)

y > -3/4 x + 3

60.

Which of the following inequalities matches the graph?

a)

x > -2

b)

x < -2

c)

y > -2

d)

y < -2

61.

3x + 5 < 5x - 9

a)

No answer

b)

7 < x

c)

x > 7

d)

7 > x

62.

Which is the solution of
-4 - 6m > -9m + 8?

a)

m < -4

b)

m > 4

c)

m < 15

d)

m > 36

63.

4x - 3 < -1x + 12

a)

x > 3

b)

x < 3

c)

x < 5

d)

x > 5

64.

You flip an inequality symbol when you...

a)

subtract

b)

multiply and divide only

c)

multiple by a negative number

d)

multiple or divide by a negative number

65.

Which number line shows the solution to:
11x + 14 < –8?

a)

a

b)

b

c)

c

d)

d

66.

Which inequality symbol describes this graph?

a)

$<$

b)

$\le$

c)

$>$

d)

$\ge$

67.

Which inequality is graphed on the given coordinate plane?

a)

y ≤ -x + 1

b)

y < x + 1

c)

y ≥ -x + 1

68.

Which of the following inequalities matches the graph?

a)

x ≤ -4

b)

x ≥ -4

c)

y ≤ -4

d)

y ≥ -4

69.

Which of the following inequalities matches the graph?

a)

x > -2

b)

x < -2

c)

y > -2

d)

y < -2

Solving and Graphing Linear and Absolute Value Inequalities

Total questions: 69

Worksheet time: 4hrs 37mins

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