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 often involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 5x - 7 ≥ 8?

Back

Add 7 to both sides: 5x ≥ 15. Then divide by 5: x ≥ 3.

Front

What is the solution to the inequality -2x + 7 < 19?

Back

Subtract 7 from both sides: -2x < 12. Then divide by -2 (remember to flip the inequality): x > -6.

Front

Solve for t in the inequality 6t + 4 ≤ -2.

Back

Subtract 4 from both sides: 6t ≤ -6. Then divide by 6: t ≤ -1.

Front

What is the solution to the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (flip the inequality): x ≥ -10.

Front

How do you solve the inequality 7k - 2 ≥ -9?

Back

Add 2 to both sides: 7k ≥ -7. Then divide by 7: k ≥ -1.

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

What is the difference between ≤ and < in inequalities?

Back

'≤' means 'less than or equal to', while '<' means 'less than' only.

Front

How do you check the solution of an inequality?

Back

Substitute the solution back into the original inequality to see if it holds true.

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.