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 2x + 6 ≥ -8?

Back

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

Front

What is the solution to the inequality -3x - 4 < 5?

Back

Add 4 to both sides: -3x < 9. Then divide by -3 (remember to flip the inequality): x > -3.

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

Solve the inequality 2 + 3x ≤ 20.

Back

Subtract 2 from both sides: 3x ≤ 18. Then divide by 3: x ≤ 6.

Front

What is the solution to the inequality -n + 8 < 26?

Back

Subtract 8 from both sides: -n < 18. Then multiply by -1 (flip the sign): n > -18.

Front

What is the difference between < and ≤?

Back

< means 'less than' and does not include the number, while ≤ means 'less than or equal to' and includes the number.

Front

How do you check the solution of an inequality?

Back

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

Front

What is the solution set for the inequality x ≥ -7?

Back

The solution set includes all numbers greater than or equal to -7.

Front

What does it mean if an inequality has no solution?

Back

It means there are no values that can satisfy the inequality, often resulting from contradictory statements.