Solving 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 7k – 2 ≥ -9?

Back

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

Front

What happens to the inequality sign when you divide by a negative number?

Back

The inequality sign flips when you divide or multiply both sides of an inequality by a negative number.

Front

Solve for x: 2x + 6 ≥ -8.

Back

Subtract 6 from both sides: 2x ≥ -14. Then divide by 2: x ≥ -7.

Front

Solve for x: -4x + 1 > 21.

Back

Subtract 1 from both sides: -4x > 20. Then divide by -4 (flip the sign): x < -5.

Front

Solve for a: -9a - 1 < 26.

Back

Add 1 to both sides: -9a < 27. Then divide by -9 (flip the sign): a > -3.

Front

What is the solution set for the inequality k ≥ -1?

Back

The solution set includes all real numbers greater than or equal to -1.

Front

What does it mean to 'flip the sign' in an inequality?

Back

Flipping the sign means changing the direction of the inequality (e.g., from > to <) when multiplying or dividing by a negative number.

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 difference between 'greater than' and 'greater than or equal to'?

Back

'Greater than' (>) means the value is strictly above, while 'greater than or equal to' (≥) includes the value itself.