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 combining like terms, adding or subtracting, and multiplying or dividing by a number.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

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

Front

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

Back

The inequality symbol flips direction.

Front

How do you graph the solution set of the inequality -4a ≤ -28?

Back

First, solve for a: a ≥ 7. Then, graph a number line with a closed circle at 7 and shade to the right.

Front

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

Back

Combine like terms: 14 < -4a + 6. Then, subtract 6 from both sides: 8 < -4a. Divide by -4 (flip the inequality): a < -2.

Front

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

Back

Combine like terms: 12x + 2 < 14. Subtract 2 from both sides: 12x < 12. Divide by 12: x < 1.

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 other side.

Front

What is the first step in solving the inequality 3x - 5 > 4?

Back

Add 5 to both sides: 3x > 9.

Front

What is the solution to the inequality 2x + 3 ≤ 11?

Back

Subtract 3 from both sides: 2x ≤ 8. Then divide by 2: x ≤ 4.

Front

How do you check the solution of an inequality?

Back

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