Free Printable Multi-step inequalities, Interval Notation, Absolute Value Equat

1.

6(n + 2) < -72

a)

n < -14

b)

n < 35/3

c)

n < -10

d)

n > -14

2.

6x + 10 > 5x - 12

a)

x > 2

b)

x < -2

c)

x < -22

d)

x > -22

3.

4(2a + 3) < 3(a - 1)

a)

a < -3

b)

a > -3

c)

a < 3

d)

a > 3

4.

-3 − 6(4x + 6) > -111

a)

x > 3

b)

x < 3

c)

x < -3

d)

x > -3

5.

Solve

2(x - 3) + 5x ≤ 9x - 14

a)

x ≥ -4

b)

x ≤ -4

c)

x ≤ 4

d)

x ≥ 4

6.

Solve:
7(x + 3) < 5x + 13

a)

x>-4

b)

x < 17

c)

x<-4

d)

x > -17

7.

Why do I draw a closed circle when it's less than or equal to or greater than or equal to?

a)

Because we are INCLUDING that solution

b)

Because we are NOT INCLUDING that solution

8.

Given:

x ≤ -10

Is -25 a solution?

a)

Yes, it is a solution.

b)

No, it is not a solution.

9.

Choose all that are not solutions of the inequality n>8

a)

12

b)

4

c)

8

d)

9

10.

When we __________ or ____________ BY a _____________, reverse the inequality symbol.

a)

add

b)

divide

c)

negative

d)

multiply

e)

positive

11.

Write the following in interval notation

x < 8

a)

[8, ∞)

b)

(8, -∞)

c)

(-∞, 8]

d)

(-∞, 8)

12.

Can you use the symbols [ or ]
with infinity?

a)

Yes

b)

No

13.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

d)

(-5, ∞)

14.

Write the following in interval notation
x ≥ 100

a)

(0, 100]

b)

(∞, 100]

c)

[100, ∞)

d)

(∞, 100)

15.

Convert into its interval notation:

$x>-9$

a)

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

b)

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

c)

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

d)

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

16.

Convert into its interval notation:

$x\le6$

a)

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

b)

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

c)

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

d)

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

17.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

d)

(-5, ∞)

18.

Solve for x
l 5x l = 40

a)

x = 8 and x =-8

b)

x = 35 and x = -35

c)

Only x = 8

d)

No Solution

19.

Solve for x
l 2x−1 l = 9

a)

x = 5 and x =-4

b)

x = 5 and x = -5

c)

Only x = 5

d)

No Solution

20.

Solve for x
l 4x−3 l = 17

a)

x = 5 and x =-3.5

b)

x = 0 and x = -5

c)

x = 10 and x = -10

d)

No Solution

21.

Solve for x
l 3x + 2 l = 5

a)

x = -2.333... and x = 1

b)

x = 4 and x = 8

c)

x = 0

d)

No Solution

22.

What is the absolute value of | 8 |?

a)

8

b)

-8

c)

0

d)

16

23.

Solve for k.

|k - 9| = -4

a)

5, 13

b)

5, -5

c)

13

d)

No solution

Multi-step inequalities, Interval Notation, Absolute Value Equat

Total questions: 23

Worksheet time: 2hrs 13mins

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