Two-Step Inequalities

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.

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

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

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

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

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

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

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

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

The first step is usually to isolate the term with the variable by adding or subtracting a constant.