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 typically involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality -6 - 3n < -36?

Back

Add 6 to both sides: -3n < -30. Then divide by -3 (remember to flip the inequality sign): n > 10.

Front

When do you flip the inequality sign?

Back

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

Front

Solve the inequality 0 ≥ -5x - 5.

Back

Add 5 to both sides: 5 ≥ -5x. Then divide by -5 (flip the sign): x ≥ -1.

Front

What is the solution to the inequality 2 - 3x ≤ 20?

Back

Subtract 2 from both sides: -3x ≤ 18. Then divide by -3 (flip the sign): x ≥ -6.

Front

How do you 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 does it mean if an inequality has no solution?

Back

An inequality has no solution when the variable cannot satisfy the inequality for any value, such as x > x.

Front

What is the difference between < and ≤ in inequalities?

Back

< means 'less than' and does not include the endpoint, while ≤ means 'less than or equal to' and includes the endpoint.

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 happens to the inequality sign when you multiply both sides by a negative number?

Back

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