Comparing Numbers: Master Inequalities in Mathematics

Question 1

Find the value of x that makes the inequality true: 2x - 5 is less than 11.

Accepted Answer

x is less than 8

Answer

x is greater than 8

Answer

x is less than 3

Answer

x is greater than 3

Question 2

Which of the following symbols represents an inequality?

Accepted Answer

>

Answer

=

Answer

+

Answer

-

Question 3

Which of the following graphs represents the inequality y ≤ 3?

Accepted Answer

A solid line at y = 3 with points below the line shaded.

Answer

A dashed line at y = 3 with points above the line shaded.

Answer

A solid line at y = 3 with points above the line shaded.

Answer

A dashed line at y = 3 with points below the line shaded.

Question 4

Translate the following statement into an inequality: The sum of x and 4 is less than 10.

Accepted Answer

x + 4 < 10

Answer

x + 4 > 10

Answer

x - 4 < 10

Answer

x - 4 > 10

Question 5

Solve the inequality: (x + 2)(x - 3) > 0. Which values of x satisfy the inequality?

Accepted Answer

x < -2 or x > 3

Answer

x < 2 or x > 3

Answer

x > -2 and x < 3

Answer

x < 2 and x > 3

Question 6

Simplify the compound inequality: x > 2 and x < 7

Accepted Answer

2 < x < 7

Answer

x < 2 or x > 7

Answer

x > 2 or x < 7

Answer

x < 7

Question 7

Find the solution to the inequality: 2(x + 1) > 5

Accepted Answer

x > 1

Answer

x > 2

Answer

x < 1

Answer

x < 2

Question 8

Which inequality represents the statement "a number x is greater than or equal to 5"?

Accepted Answer

x ≥ 5

Answer

x > 5

Answer

x < 5

Answer

x ≤ 5

Question 9

Which of the following inequalities is correct?

Accepted Answer

15 is greater than or equal to 12

Answer

3 is greater than 5

Answer

5 is equal to 2

Answer

10 is less than 10

Question 10

Translate this sentence into an inequality: The sum of x and 5 is less than 12.

Accepted Answer

x + 5 < 12

Answer

x - 5 < 12

Answer

x - 5 > 12

Answer

x + 5 > 12

Question 11

Graph the inequality x + 3 ≥ 5 on a number line:

Accepted Answer

[Image of a number line with a closed circle at 2 and an arrow pointing to the right]

Answer

[Image of a number line with a closed circle at -2 and an arrow pointing to the right]

Answer

[Image of a number line with an open circle at 2 and an arrow pointing to the left]

Answer

[Image of a number line with an open circle at -2 and an arrow pointing to the left]

Question 12

Which inequality is equivalent to 3x - 1 > 7?

Accepted Answer

x is greater than 2

Answer

x is greater than 3

Answer

x is less than 2

Answer

x is less than 3

Question 13

What type of inequality has an open circle on the number line?

Accepted Answer

Less than

Answer

Less than or equal to

Answer

Greater than

Answer

Greater than or equal to

Question 14

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

Accepted Answer

x + 5 > 10

Answer

10 > x + 5

Answer

x - 5 > 10

Answer

5 - x > 10

Question 15

If a number, let's call it 'x', is less than or equal to 5, which of these shows it correctly?

Accepted Answer

x ≤ 5

Answer

x > 5

Answer

x ≥ 5

Answer

x < 5

Question 16

Translate the statement "The sum of x and 5 is greater than or equal to 10" into a mathematical inequality.

Accepted Answer

x + 5 > 10

Answer

x + 5 < 10

Answer

5 - x > 10

Question 17

Identify the option that is NOT an inequality.

Accepted Answer

y = 4

Answer

5 > 7

Answer

x < 3

Answer

2 ≤ 10

Question 18

Which image represents the graph of the inequality x ≥ 4?

Accepted Answer

[Image of a number line with a closed circle at 4 and an arrow pointing to the right]

Answer

[Image of a number line with an open circle at 4 and an arrow pointing to the right]

Answer

[Image of a number line with a closed circle at 4 and an arrow pointing to the left]

Answer

[Image of a number line with an open circle at 4 and an arrow pointing to the left]

Question 19

Find the inverse inequality of 2x - 5 < 1.

Accepted Answer

x > 3

Answer

x < 3

Answer

2x - 5 > 1

Answer

2x - 5 < -1

Question 20

Which inequality has the same solution set as 3(x - 2) ≥ 6?

Accepted Answer

x ≥ 4

Answer

x ≥ 0

Answer

x ≤ 0

Answer

x ≤ 4

Question 21

Which inequality is equivalent to |2x - 5| ≥ 3?

Accepted Answer

2x - 5 ≤ -3 or 2x - 5 ≥ 3

Answer

2x - 5 ≥ -3 and 2x - 5 ≤ 3

Answer

2x ≤ 8 or 2x ≥ 2

Answer

2x ≥ 8 and 2x ≤ 2

Question 22

Which of the following is not a characteristic of an inequality?

Accepted Answer

Is always a true statement

Answer

Uses symbols like <, >, ≤, or ≥

Answer

Describes a range of values

Answer

Can be graphed on a number line

Question 23

Which of the following inequalities represents the statement 'The number y is at most 10'?

Accepted Answer

y ≤ 10

Answer

y ≥ 10

Answer

y < 10

Answer

y > 10

Question 24

Which of the following is an example of how inequalities are used in real life?

Accepted Answer

Setting limits on a budget

Answer

Predicting the weather

Answer

Finding the area of a triangle

Answer

Calculating the volume of a cube

Question 25

The height of a tree is less than 20 feet. Which inequality represents this situation?

Accepted Answer

T < 20

Answer

T > 20

Answer

T ≥ 20

Answer

T ≤ 20

Question 26

Which inequality matches the statement 'x is a number greater than 5'?

Accepted Answer

x > 5

Answer

x < 5

Answer

x ≥ 5

Answer

x ≤ 5

Question 27

In the inequality a < b, which number is smaller?

Accepted Answer

a

Answer

b

Answer

Cannot be determined

Question 28

Which symbol means 'not less than'?

Accepted Answer

≥

Answer

>

Answer

≤

Question 29

Solve for x: 3(x - 2) > 12

Accepted Answer

x > 8

Answer

x < 8

Answer

x > 6

Answer

x < 6

Question 30

Which inequality has a solution set of all real numbers less than 2?

Accepted Answer

x < 2

Answer

x ≤ 2

Answer

x ≥ 2

Answer

x > 2

Question 31

Create an inequality that represents the statement: 'The sum of x and 7 is at least 15'.

Accepted Answer

x + 7 ≥ 15

Answer

x + 7 ≤ 15

Answer

x - 7 ≤ 15

Answer

x - 7 ≥ 15

Question 32

What does the inequality x < y tell us about the relationship between x and y?

Accepted Answer

x is less than y

Answer

y is less than x

Answer

x is greater than or equal to y

Answer

y is greater than or equal to x

Question 33

Which inequality represents the statement 'The sum of x and 5 is at least 10'?

Accepted Answer

x + 5 ≥ 10

Answer

10 ≥ x + 5

Answer

x + 5 ≤ 10

Answer

5 ≥ x + 10

Question 34

Solve the inequality: 2x - 5 > 7

Accepted Answer

x > 6

Answer

x ≥ 6

Answer

x < 6

Question 35

Graph the inequality: x ≤ -2

Accepted Answer

A closed circle at -2 and shading to the left on a number line

Answer

A closed circle at -2 and shading to the right on a number line

Answer

An open circle at -2 and shading to the right on a number line

Question 36

Which symbol represents 'less than or equal to' in an inequality?

Accepted Answer

≤

Answer

=

Answer

>

Answer

<

Question 37

Write the inequality that represents the statement: 'The temperature is above freezing, which is 32 degrees Fahrenheit'

Accepted Answer

T > 32

Answer

32 ≤ T

Answer

32 > T

Answer

T ≥ 32

Question 38

Solve the inequality: |x| < 4

Accepted Answer

-4 < x < 4

Answer

x < -4 or x > 4

Answer

|x| > 4

Answer

|x| = 4

Question 39

Which inequality represents the statement: 'Two times a number minus 5 is greater than or equal to 10'?

Accepted Answer

2x - 5 ≥ 10

Answer

10 ≥ 2x - 5

Answer

10 ≤ 2x - 5

Answer

2x - 5 ≤ 10

Question 40

Which inequality represents numbers that are greater than negative three?

Accepted Answer

x > -3

Answer

x ≥ -3

Answer

x ≤ -3

Answer

x < -3

Question 41

A store sells shirts for $15 each. If you have $50, which inequality shows how many shirts, 's', you can buy?

Accepted Answer

15s ≤ 50

Answer

15s < 50

Answer

15s ≥ 50

Answer

15s > 50

Question 42

Which inequality means 'x is greater than 5'?

Accepted Answer

x > 5

Answer

5 > x

Answer

5 < x

Answer

x < 5

Question 43

What is the solution to the inequality 2x - 5 < 15?

Accepted Answer

x < 10

Answer

x > 5

Answer

x > 10

Answer

x < 5

Question 44

How do you graph the inequality y ≥ 3 on a number line?

Accepted Answer

A closed circle at 3 with a line extending to the right.

Answer

An open circle at 3 with a line extending to the right.

Answer

A closed circle at 3 with a line extending to the left.

Answer

An open circle at 3 with a line extending to the left.

Question 45

Which of these is NOT a type of inequality?

Accepted Answer

Equality

Answer

Linear

Answer

Absolute value

Answer

Quadratic

Question 46

What is the solution to the compound inequality -2 < x + 3 ≤ 5?

Accepted Answer

-5 < x ≤ 2

Answer

-2 < x ≤ 5

Answer

x > -5

Answer

x < 2

Question 47

What is the solution to the inequality |x - 2| > 5?

Accepted Answer

x < -3 or x > 7

Answer

3 < x < 7

Answer

x < 3 or x > 7

Answer

-3 < x < 7

Question 48

If 3x - 2 > 11, what is the value of x?

Accepted Answer

x > 4

Answer

x < 11

Answer

x < 4

Answer

x > 11