7.3D2: 2 Step Inequality

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 (remember to flip the inequality sign): x ≥ -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

What does an open circle represent on a graph of an inequality?

Back

An open circle indicates that the number is not included in the solution set (e.g., x < 4).

Front

What does a closed circle represent on a graph of an inequality?

Back

A closed circle indicates that the number is included in the solution set (e.g., x ≤ 4).

Front

Solve and graph the inequality: 7n - 1 > 76.

Back

Add 1 to both sides: 7n > 77. Then divide by 7: n > 11. Graph with an open circle at 11.

Front

What is the solution to the inequality -3x ≥ 12?

Back

Divide by -3 (flip the sign): x ≤ -4.

Front

What is the first step in solving the inequality 5x - 3 < 12?

Back

Add 3 to both sides: 5x < 15.

Front

What is the final step in solving the inequality 5x < 15?

Back

Divide by 5: x < 3.

Front

What is the solution to the inequality 2x + 6 ≤ 18?

Back

Subtract 6 from both sides: 2x ≤ 12. Then divide by 2: x ≤ 6.