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 x/4 ≤ 8?

Back

Multiply both sides by 4: x ≤ 32.

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

What does a closed dot on a graph represent?

Back

A closed dot represents that the number is included in the solution set, used for ≤ and ≥.

Front

What does an open dot on a graph represent?

Back

An open dot represents that the number is not included in the solution set, used for < and >.

Front

How do you graph the inequality a ≥ 11?

Back

Draw a closed dot at 11 and shade to the right.

Front

How do you graph the inequality a < 11?

Back

Draw an open dot at 11 and shade to the left.

Front

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

Back

x > -3.

Front

What is the first step to solve the inequality -3x ≥ 12?

Back

Divide both sides by -3 and flip the inequality sign: x ≤ -4.

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.