Solve 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 -4x + 14 ≤ 54?

Back

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

Front

What does the solution x ≥ -10 mean in a graph?

Back

It means that the solution includes all numbers greater than or equal to -10, represented by a solid dot at -10 and a line extending to the right.

Front

How do you solve the inequality 2x + 6 ≥ -8?

Back

Subtract 6 from both sides: 2x ≥ -14. Then divide by 2: x ≥ -7.

Front

What does the solution x ≥ -7 indicate?

Back

It indicates that x can be any number greater than or equal to -7.

Front

How do you solve the inequality -9a - 1 < 26?

Back

Add 1 to both sides: -9a < 27. Then divide by -9 (flip the inequality): a > -3.

Front

What does the solution a > -3 represent?

Back

It represents all numbers greater than -3, shown with an open dot at -3 and a line extending to the right.

Front

How do you solve the inequality 3 + 9k > 111?

Back

Subtract 3 from both sides: 9k > 108. Then divide by 9: k > 12.

Front

What does the solution k > 12 mean?

Back

It means k can be any number greater than 12.

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.