Solving Inequalities Quiz: Test Your Skills - 9th Grade Math

Question 1

Which of the following inequalities represents the solution to 2x - 5 > 3?

Accepted Answer

x > 4

Answer

x ≤ 4

Answer

x ≥ 4

Answer

x < 4

Question 2

What is the solution to the inequality -3x + 6 ≤ 12?

Accepted Answer

x ≥ -2

Answer

x ≤ -2

Answer

x > -2

Answer

x < -2

Question 3

Which graph represents the solution to the inequality x + 2 > 5?

Accepted Answer

A number line with an open circle at 3 and shaded to the right

Answer

A number line with a closed circle at 3 and shaded to the right

Answer

A number line with an open circle at 3 and shaded to the left

Question 4

If 4y - 7 < 13, what is the maximum possible integer value of y?

Accepted Answer

5

Answer

2

Answer

4

Answer

3

Question 5

Which of the following is NOT a valid step in solving an inequality?

Accepted Answer

Adding a different constant to both sides of the inequality.

Answer

Subtracting the same constant from both sides of the inequality.

Answer

Multiplying both sides of the inequality by the same positive number.

Question 6

The inequality 2x + 3 ≤ 9 can be rewritten as...

Accepted Answer

x ≤ 3

Answer

x = 3

Answer

x ≥ 3

Question 7

A store sells shirts for $15 each and pants for $25 each. You want to buy at least one of each and spend no more than $100. Which inequality represents this situation, where 's' is the number of shirts and 'p' is the number of pants?

Accepted Answer

15s + 25p ≤ 100, s ≥ 1, p ≥ 1

Answer

15s + 25p > 100, s ≥ 1, p ≥ 1

Answer

15s + 25p > 100, s = 1, p = 1

Answer

15s + 25p ≤ 100, s < 1, p < 1

Question 8

Which of the following is equivalent to the inequality 2x - 5 < 11?

Accepted Answer

x < 8

Answer

x > 8

Answer

x < 16

Answer

2x < 16

Question 9

Which of the following represents the solution set of the inequality x^2 - 4 > 0?

Accepted Answer

(x < -2) U (x > 2)

Answer

(x < -2) U (x < 2)

Answer

(x > 2) U (x < 4)

Answer

(x > -2) U (x > 2)

Question 10

If the sum of two numbers is at least 15, write an inequality to represent this situation.

Accepted Answer

x + y ≥ 15

Answer

x - y ≥ 15

Answer

x + y = 15

Question 11

Which of the following graphs represents the inequality y < 2x + 1?

Accepted Answer

[Image of a line with slope 2 and y-intercept 1, shaded below the line]

Answer

[Image of a line with slope 2 and y-intercept 1, shaded above the line]

Answer

[Image of a line with slope -2 and y-intercept 1, shaded below the line]

Question 12

Solve the inequality: (x - 2)(x + 1) > 0

Accepted Answer

x < -1 or x > 2

Answer

x > -1 or x < 2

Answer

x < 1 or x > -2

Question 13

Solve the inequality: 1/3(x - 2) > 4

Accepted Answer

x > 8

Answer

x < 8

Answer

x > 14

Answer

x < 14

Question 14

Which inequality represents the solution set {x | x < 5}?

Accepted Answer

x < 5

Answer

x > 5

Answer

x ≥ 5

Answer

x ≤ 5

Question 15

Solve the inequality: 2x + 5 > 15

Accepted Answer

x > 5

Answer

x ≤ 5

Answer

x < 5

Answer

x ≥ 5

Question 16

Which value of x makes the inequality true: 3(x - 2) ≤ 6?

Accepted Answer

x ≤ 4

Answer

x < 4

Answer

x > 4

Answer

x ≥ 4

Question 17

Solve the inequality: |x - 3| > 2

Accepted Answer

x < 1 or x > 5

Answer

x > 1

Answer

x > 3

Answer

x < 5

Question 18

Which of the following is equivalent to the inequality 2x - 5 > 7?

Accepted Answer

x > 6

Answer

x < 6

Answer

x > 12

Answer

2x > 12

Question 19

Solve the compound inequality: -2 < x + 3 ≤ 5

Accepted Answer

-5 < x ≤ 2

Answer

-5 ≤ x ≤ 2

Answer

-2 ≤ x ≤ 5

Answer

-2 < x < 2

Question 20

Which inequality represents the shaded region on the number line?

Accepted Answer

x ≤ 0 or x > 2

Answer

x < 0 or x ≥ 2

Answer

0 ≤ x ≤ 2

Answer

x > 0 or x < 2

Question 21

Solve the inequality: (x + 2)(x - 3) < 0

Accepted Answer

-2 < x < 3

Answer

x > -2 or x < 3

Answer

-2 ≤ x ≤ 3

Answer

x < -2 or x > 3

Question 22

Which of the following is true about the inequality x² - 4 < 0?

Accepted Answer

The solution set is empty.

Answer

The solution set is -2 < x < 2

Answer

The solution set is x < -2 or x > 2

Answer

The solution set is all real numbers.

Question 23

Which inequality represents the set of numbers that are at least 5 but less than 10?

Accepted Answer

5 ≤ x < 10

Answer

5 ≤ x ≤ 10

Answer

5 < x ≤ 10

Answer

5 < x < 10

Question 24

Solve the inequality 2x - 5 > 9.

Accepted Answer

x > 7

Answer

x > -7

Answer

x < 7

Answer

x < -7

Question 25

Which of the following represents the solution set of the inequality x + 3 < 0?

Accepted Answer

{x | x < -3}

Answer

{x | x > 3}

Answer

{x | x < 3}

Answer

{x | x > -3}

Question 26

Solve the inequality 2(x - 1) + 3 > 7.

Accepted Answer

x > 3

Answer

x < 1

Answer

x < 3

Answer

x > 1

Question 27

Find the solution set of the inequality -3x > 15.

Accepted Answer

{x | x < -5}

Answer

{x | x > -5}

Answer

{x | x > 5}

Answer

{x | x < 5}

Question 28

Which of the following intervals represents the solution set of the inequality -2 < x + 1 ≤ 5?

Accepted Answer

(-1, 4]

Answer

[-1, 4)

Answer

[0, 5]

Answer

(0, 5]

Question 29

Solve the inequality |x - 2| > 5.

Accepted Answer

x < -3 or x > 7

Answer

x < 3 or x > 7

Answer

x > 3 or x < 7

Answer

x > -3 or x < 7

Question 30

Which value of x satisfies the inequality 3(2 - x) - 2(x + 1) ≥ 8?

Accepted Answer

-3

Answer

3

Answer

-5

Answer

5

Question 31

The sum of two numbers is less than 20. If one of the numbers is x, which of the following represents the other number?

Accepted Answer

20 - x

Answer

x - 20

Answer

-20 - x

Answer

x + 20

Question 32

Which of the following inequalities is equivalent to x² < 4?

Accepted Answer

-2 < x < 2

Answer

-4 < x < 4

Answer

2 < x < 4

Question 33

The width of a rectangle is 3 inches less than its length. If the perimeter of the rectangle is less than 30 inches, what is the maximum possible length of the rectangle?

Accepted Answer

7.5 inches

Answer

12.5 inches

Answer

10 inches