Multi-Step Inequalities

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division.

Front

How do you solve the inequality 3(2z - 5) < 12?

Back

First, distribute: 6z - 15 < 12. Then, add 15 to both sides: 6z < 27. Finally, divide by 6: z < 4.5.

Front

What happens to the inequality symbol when you multiply or divide by a negative number?

Back

The inequality symbol flips direction.

Front

Solve the inequality -4x + 14 ≤ 54.

Back

Subtract 14 from both sides: -4x ≤ 40. Then, divide by -4 (flipping the inequality): x ≥ -10.

Front

What is the solution to the inequality 14 < -2a + 6 - 2a?

Back

Combine like terms: 14 < -4a + 6. Subtract 6: 8 < -4a. Divide by -4 (flipping the inequality): a < -2.

Front

Solve the inequality -3 − 6(4x + 6) > -111.

Back

Distribute: -3 - 24x - 36 > -111. Combine like terms: -24x > -72. Divide by -24: x < 3.

Front

What does it mean to isolate the variable in an inequality?

Back

Isolating the variable means to manipulate the inequality so that the variable is on one side and all other terms are on the opposite side.

Front

What is the first step in solving the inequality 5x - 3 < 12?

Back

Add 3 to both sides: 5x < 15.

Front

How do you check the solution of an inequality?

Back

Substitute the solution back into the original inequality to see if it holds true.

Front

What is the solution set for the inequality x + 4 > 10?

Back

Subtract 4 from both sides: x > 6.