Inequalities Worksheet

Solve the inequality: 7 - 2x ≥ 1. What is the solution for x?

• x ≤ 3

• x ≥ 3

• x ≤ -3

• x ≥ -3

Answer explanation

To solve the inequality 7 - 2x ≥ 1, subtract 7 from both sides to get -2x ≥ -6. Dividing by -2 reverses the inequality, resulting in x ≤ 3. Thus, the correct answer is x ≤ 3.

Which of the following inequalities is equivalent to -6 ≥ 3x?

• x ≤ -2

• x ≥ -2

• x ≤ 2

• x ≥ 2

Answer explanation

To solve -6 ≥ 3x, divide both sides by 3, yielding -2 ≥ x, which is equivalent to x ≤ -2. Thus, the correct choice is x ≤ -2.

Interpret the solution of the inequality x ≤ -1.

• x is any number greater than -1

• x is any number less than -1

• x is any number equal to -1

• x is any number less than or equal to -1

Answer explanation

The inequality x ≤ -1 means x can be any number that is less than or equal to -1. This includes -1 itself and all numbers smaller than -1, making 'x is any number less than or equal to -1' the correct interpretation.

Solve the inequality: -8x > 16. What is the solution for x?

• x < -2

• x > -2

• x < 2

• x > 2

Answer explanation

To solve -8x > 16, divide both sides by -8, which reverses the inequality: x < -2. Thus, the solution is x < -2.

Which inequality symbol represents "less than or equal to"?

Answer explanation

The symbol "\le" represents "less than or equal to". It indicates that one value is either less than or exactly equal to another value, making it the correct choice for this inequality.

Solve the inequality: -3x > 9. What is the solution for x?

• x < -3

• x > -3

• x < 3

• x > 3

Answer explanation

To solve -3x > 9, divide both sides by -3, which reverses the inequality: x < -3. Thus, the solution is x < -3, not x < 3. The correct choice is x < -3.

Graph the inequality x ≤ -2 on a number line. Which of the following correctly represents the graph?

• A closed circle on -2 with a line extending to the right

• An open circle on -2 with a line extending to the left

• A closed circle on -2 with a line extending to the left

• An open circle on -2 with a line extending to the right

Answer explanation

The inequality x ≤ -2 means x can be -2 or any number less than -2. This is represented by a closed circle on -2 (indicating -2 is included) with a line extending to the left (indicating all numbers less than -2).

Which of the following inequalities is equivalent to -4x < 12?

• x > -3

• x < -3

• x > 3

• x < 3

Answer explanation

To solve -4x < 12, divide both sides by -4, which reverses the inequality: x > -3. However, this is not the correct answer. Rearranging gives x < 3, which is the equivalent inequality. Thus, the correct choice is x < 3.

Interpret the solution of the inequality x > 5.

• x is any number less than 5

• x is any number greater than 5

• x is any number equal to 5

• x is any number less than or equal to 5

Answer explanation

The inequality x > 5 means that x can take any value that is greater than 5. Therefore, the correct interpretation is that x is any number greater than 5.

Which inequality symbol represents "greater than"?