Inequalities Worksheets

Solve the inequality: -5 ≤ 2x - 3. What is the solution for x?

• x ≥ 1

• x ≤ 1

• x ≥ -1

• x ≤ -1

Answer explanation

To solve -5 ≤ 2x - 3, add 3 to both sides: -2 ≤ 2x. Then, divide by 2: -1 ≤ x, or x ≥ -1. Thus, the solution is x ≥ -1.

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.

When you multiply or divide both sides of an inequality by a negative number, what must you do to the inequality symbol?

• Leave it unchanged

• Reverse it

• Change it to an equal sign

• Add a negative sign

Answer explanation

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol. This ensures the inequality remains true, making 'Reverse it' the correct choice.

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).