Two-Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. It often involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality -8k - 4 ≤ -60?

Back

Add 4 to both sides: -8k ≤ -56. Then divide by -8 (remember to flip the inequality): k ≥ 7.

Front

What does the solution k ≥ 7 mean in a real-world context?

Back

It means that the value of k must be 7 or greater to satisfy the inequality.

Front

How do you solve the inequality u/7 - 1 ≤ 1?

Back

Add 1 to both sides: u/7 ≤ 2. Then multiply by 7: u ≤ 14.

Front

What is the solution to the inequality 7n - 1 > 76?

Back

Add 1 to both sides: 7n > 77. Then divide by 7: n > 11.

Front

What does the solution 3 < c indicate?

Back

It indicates that the value of c must be greater than 3.

Front

How do you solve the inequality 6t + 4 ≤ -2?

Back

Subtract 4 from both sides: 6t ≤ -6. Then divide by 6: t ≤ -1.

Front

What is the first step in solving a two-step inequality?

Back

The first step is usually to isolate the term with the variable by performing the opposite operation (addition or subtraction).

Front

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

Back

The inequality sign flips when you multiply or divide both sides by a negative number.

Front

What is the graphical representation of an inequality?

Back

It is shown on a number line with an open or closed circle indicating whether the endpoint is included or excluded.