Solving 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, typically involving 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 (flip the sign): x ≥ -10.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

Front

Solve the inequality -9a - 1 < 26.

Back

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

Front

What is the solution to the inequality 11 > -3y + 2?

Back

Subtract 2 from both sides: 9 > -3y. Then divide by -3 (flip the sign): -3 < y.

Front

When do you flip the sign in an inequality?

Back

You flip the sign when you multiply or divide both sides of the inequality by a negative number.

Front

Solve the inequality -3x ≥ 12.

Back

Divide by -3 (flip the sign): x ≤ -4.

Front

What is the solution to the inequality -3x - 4 < 5?

Back

Add 4 to both sides: -3x < 9. Then divide by -3 (flip the sign): x > -3.

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 adding or subtracting a constant from both sides.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'.