Master Inequalities: Conquer One-Step, Two-Step, and Multi-Step Challenges

Question 1

Which of the following inequalities represents the statement "The sum of x and 5 is greater than 10"?

Accepted Answer

x + 5 > 10

Answer

x + 5 < 10

Answer

x - 5 > 10

Answer

x - 5 < 10

Question 2

Which of the following inequalities is equivalent to 3(x - 1) > 9?

Accepted Answer

x - 1 > 3

Answer

x - 1 < 3

Answer

x + 1 > 3

Answer

x + 1 < 3

Question 3

Which of the following inequalities represents the statement "The product of x and y is less than or equal to 10"?

Accepted Answer

xy ≤ 10

Answer

xy ≥ 10

Answer

xy < 10

Answer

xy > 10

Question 4

Solve the system of inequalities: x + y < 5, x - y > 1

Accepted Answer

x < 3, y > 2

Answer

x < 2, y < 3

Answer

x > 2, y > 3

Answer

x > 3, y < 2

Question 5

Which of the following is the solution set of the inequality (x + 3)² - 9 < 0?

Accepted Answer

x < -6 or x > 0

Answer

x < -6 or x < 0

Answer

x > -6 and x < 0

Answer

x > -6 and x > 0

Question 6

Solve the inequality: 2x - 5 is greater than 11.

Accepted Answer

x is greater than 8

Answer

x is less than 8

Answer

x is greater than 6

Answer

x is less than 6

Question 7

Solve the inequality: x - 5 is less than 2.

Accepted Answer

x is less than 3

Answer

x is greater than 3

Answer

x is less than -3

Answer

x is greater than -3

Question 8

Which of the following is NOT a solution to the inequality: x + 1.5 is greater than 2.5?

Accepted Answer

2

Answer

3

Answer

4

Answer

5

Question 9

Which of the following inequalities represents the statement: 'The number x is at least -10'?

Accepted Answer

x is greater than or equal to -10

Answer

x is less than or equal to -10

Answer

x is less than -10

Answer

x is greater than -10

Question 10

Solve the inequality: 3x - 5 < 10

Accepted Answer

x < 5

Answer

x > 5

Answer

x < 15

Answer

x > 15

Question 11

Solve the inequality: 3/4 x - 1 < 2

Accepted Answer

x < 4

Answer

x > 4

Answer

x < 8

Answer

x > 8

Question 12

Which inequality represents the statement: "The sum of x and 5 is greater than 10"?

Accepted Answer

x + 5 > 10

Answer

x + 5 < 10

Answer

5 - x > 10

Answer

5 - x < 10

Question 13

Solve the absolute value inequality: |x - 2| ≤ 3

Accepted Answer

-3 ≤ x ≤ 5

Answer

-1 ≤ x ≤ 5

Answer

-5 ≤ x ≤ 1

Answer

-5 ≤ x ≤ -1

Question 14

Which of the following inequality symbols represents 'greater than or equal to'?

Accepted Answer

Greater than or equal to (>=)

Answer

Less than (<)

Answer

Greater than (>)

Answer

Less than or equal to (<=)

Question 15

Solve the inequality: 2x - 5 > 9

Accepted Answer

x is greater than 7

Answer

x is greater than 2

Answer

x is less than 2

Answer

x is less than 7

Question 16

Which of the following is NOT a solution to the inequality: 2x - 3 > 7?

Accepted Answer

7

Answer

4

Answer

5

Answer

6

Question 17

Which of the following is a true statement about the inequality: 5x + 2 > 3x - 1?

Accepted Answer

The inequality has infinitely many solutions.

Answer

The inequality has no solution.

Answer

The inequality has one solution.

Answer

The inequality has two solutions.

Question 18

Which symbol correctly represents 'x is less than or equal to 5'?

Accepted Answer

x <= 5

Answer

x > 5

Answer

x < 5

Answer

x >= 5

Question 19

Solve the inequality: 2x + 5 > 11

Accepted Answer

x > 3

Answer

x < 3

Answer

x > -3

Answer

x < -3

Question 20

Solve for x: 1/3(x - 6) > 4

Accepted Answer

x > 18

Answer

x < 18

Answer

x > -18

Answer

x < -18

Question 21

Solve for x: |x - 2| < 3

Accepted Answer

-1 < x < 5

Answer

x < -1 or x > 5

Answer

x > -1 or x < 5

Answer

x < 1 or x > -1

Question 22

Solve the inequality: x + 3 > 7

Accepted Answer

x > 4

Answer

x < 4

Answer

x < 10

Answer

x > 10

Question 23

Which of the following is NOT a solution to the inequality x² - 4 < 0?

Accepted Answer

4

Answer

-2

Answer

0

Answer

2

Question 24

Solve the system of inequalities: x + y ≥ 5, x - y ≤ 1

Accepted Answer

x ≥ 2, y ≥ 3

Answer

x ≤ 2, y ≤ 3

Answer

x ≥ 3, y ≥ 2

Answer

x ≤ 3, y ≤ 2

Question 25

Solve the inequality: 2x + 3 > 5 and x - 1 < 2

Accepted Answer

x > 2 and x < 4

Answer

x > 2 and x > 4

Answer

x < 2 and x < 4

Answer

x < 2 and x > 4

Question 26

Graph the inequality: x > 2 on the number line

Accepted Answer

A line with an open circle at x = 2 and an arrow pointing right

Answer

A line with a closed circle at x = 2 and an arrow pointing right

Answer

A line with an open circle at x = 2 and an arrow pointing left

Answer

A line with a closed circle at x = 2 and an arrow pointing left

Question 27

Solve the inequality: x + 3 < 7

Accepted Answer

x < 4

Answer

x < 10

Answer

x > 4

Answer

x > 10

Question 28

Solve the inequality: 2/3x + 1 > 5

Accepted Answer

x > 6

Answer

x < 6

Answer

x > 12

Answer

x < 12

Question 29

Solve the inequality: 3(x - 2) > 12 and provide clear steps to demonstrate your solution.

Accepted Answer

x > 8

Answer

x < 8

Answer

x < 6

Question 30

Solve the inequality: 2/3x < 6 and provide a clear and detailed solution.

Accepted Answer

x < 9

Answer

x < 3

Answer

x > 3

Answer

x > 9

Question 31

Which of the following inequalities correctly represents the statement "The sum of x and y is at most 10"?

Accepted Answer

x + y ≤ 10

Answer

x + y ≥ 10

Answer

x + y > 10

Answer

x + y < 10

Question 32

Solve for x: 2x - 5 ≥ 9

Accepted Answer

x ≥ 7

Answer

x ≥ -7

Answer

x ≤ 7

Answer

x ≤ -7

Question 33

Solve for x: |x - 2| ≥ 5

Accepted Answer

x ≤ -3 or x ≥ 7

Answer

x < -3 or x > -7

Answer

x > 3 and x < -7

Answer

x > -3 and x < 7

Question 34

Which inequality represents the set of all real numbers greater than or equal to zero?

Accepted Answer

x ≥ 0

Answer

x < 0

Answer

x > 1

Answer

x ≤ 0

Question 35

Solve the following inequality: 3x - 7 < 14

Accepted Answer

x < 7

Answer

x > -7

Answer

x > 7

Answer

x < -7

Question 36

Solve the inequality: 0.25x + 0.75 > 1.5

Accepted Answer

x > 3

Answer

x < -3

Answer

x < 3

Answer

x > -3

Question 37

Convert the inequality x ≤ 4 to its equivalent form.

Accepted Answer

4 ≥ x

Answer

-x ≤ 4

Answer

x > 4

Answer

-x ≥ 4

Question 38

Solve the absolute value inequality: |2x - 5| ≥ 3

Accepted Answer

x ≤ 1 or x ≥ 4

Answer

-x ≤ 1 or -x ≥ 4

Answer

x ≥ 1 and x ≤ 4

Answer

x ≥ -1 and x ≤ -4

Question 39

Solve the inequality:  *x* + 5 > 12

Accepted Answer

x > 7

Answer

x < 7

Answer

x > 17

Answer

x < 17

Question 40

Which inequality represents the phrase 'The product of a number and 3 is less than or equal to 15'?

Accepted Answer

3x ≤ 15

Answer

3x < 15

Answer

x + 3 ≤ 15

Answer

3x ≥ 15

Question 41

Solve for *x*: -2*x* + 7 < 15

Accepted Answer

x > -4

Answer

x > -11

Answer

x < -11

Answer

x < -4

Question 42

Which of these numbers is a solution to the inequality: 2*x* - 1 ≥ 5?

Accepted Answer

4

Answer

-3

Answer

1

Answer

2

Question 43

Solve and graph the solution set of: 4(*x* - 2) < 20

Accepted Answer

x < 7

Answer

x < 3

Answer

x > 7

Answer

x > 3

Question 44

Which inequality represents all numbers less than -5?

Accepted Answer

x < -5

Answer

x ≤ -5

Answer

x ≥ -5

Answer

x > -5

Question 45

Solve for *x*: -1/3*x* ≤ 2

Accepted Answer

x ≥ -6

Answer

x ≤ -6

Answer

x ≤ 6

Answer

x ≥ 6

Question 46

Which inequality represents the phrase 'a number, *x*, is less than or equal to 5'?

Accepted Answer

x ≤ 5

Answer

x ≥ 5

Answer

x > 5

Answer

x < 5

Question 47

Solve the inequality: 3*x* + 2 > 11

Accepted Answer

x > 3

Answer

x ≤ 3

Answer

x < 3

Answer

x ≥ 3

Question 48

Solve the inequality: 2(*x* - 4) ≤ 6

Accepted Answer

x ≤ 7

Answer

x ≥ 7

Answer

x ≤ 1

Answer

x ≥ 1

Question 49

Which graph represents the solution to the inequality -2x + 5 < 1?

Accepted Answer

A number line with an open circle at x = 2 and shading to the right.

Answer

A number line with an open circle at x = 2 and shading to the left.

Answer

A number line with a closed circle at x = 2 and shading to the right.

Answer

A number line with a closed circle at x = 2 and shading to the left.

Question 50

Solve the inequality:  1/2x + 3 > 5

Accepted Answer

x > 4

Answer

x ≤ 4

Answer

x < 4

Answer

x ≥ 4

Question 51

Which inequality represents the shaded region on the graph?

Accepted Answer

y > 2x - 1

Answer

y ≤ 2x - 1

Answer

y ≥ 2x - 1

Answer

y < 2x - 1

Question 52

You want to buy at least 5 items, a mix of t-shirts and sweatshirts, from a store. T-shirts cost $10 each and sweatshirts cost $20 each.  You have a budget of $80. Which system of inequalities represents this situation?

Accepted Answer

t + s ≥ 5 and 10t + 20s ≤ 80

Answer

t + s ≥ 5 and 10t + 20s ≥ 80

Answer

t + s ≤ 5 and 10t + 20s ≤ 80

Answer

t + s ≤ 5 and 10t + 20s ≥ 80

Question 53

Solve for *x* in the inequality: 0.5x - 1.2 > 2.8

Accepted Answer

x > 8

Answer

x ≥ 8

Answer

x ≤ 8

Answer

x < 8

Question 54

Which inequality represents the solution set shown on the number line, where a closed circle is at -3 and the shading is to the left?

Accepted Answer

x ≤ -3

Answer

x < -3

Answer

x ≥ -3

Answer

x > -3

Question 55

A car rental company charges a flat fee of $25 plus $0.30 per mile driven. You have a budget of $100.  Which inequality represents the maximum number of miles (*m*) you can drive?

Accepted Answer

0.30m + 25 ≤ 100

Answer

0.30m + 25 ≥ 100

Answer

0.30m - 25 ≥ 100

Answer

0.30m - 25 ≤ 100