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. For example, in the inequality 2x + 3 < 7, you would first subtract 3 from both sides and then divide by 2.

Front

How do you solve the inequality -169 ≤ 8m - 9?

Back

Add 9 to both sides: -160 ≤ 8m. Then divide by 8: -20 ≤ m. The solution is m ≥ -20.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves representing the solution set on a number line, using an open or closed circle to indicate whether the endpoint is included.

Front

What is the solution to the inequality 5 + x ≥ 29?

Back

Subtract 5 from both sides: x ≥ 24. The solution is x ≥ 24.

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 is the solution to the inequality 3x ≥ 12?

Back

Divide both sides by 3: x ≥ 4. The solution is x ≥ 4.

Front

How do you solve the inequality 77 ≤ 5 + 8n?

Back

Subtract 5 from both sides: 72 ≤ 8n. Then divide by 8: 9 ≤ n. The solution is n ≥ 9.

Front

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

Back

Divide both sides by -3 (flip the sign): x ≤ -4. The solution is x ≤ -4.

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution if there are no values that satisfy the inequality, such as x < x.

Front

What is the difference between a closed circle and an open circle on a number line?

Back

A closed circle indicates that the number is included in the solution (≤ or ≥), while an open circle indicates that the number is not included (< or >).