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. It typically involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 2k - 9 ≤ -19?

Back

Add 9 to both sides: 2k ≤ -10. Then divide by 2: k ≤ -5.

Front

What does the solution k ≤ -5 represent on a number line?

Back

It represents all numbers less than or equal to -5, including -5 itself.

Front

How do you solve the inequality -4x + 1 > 21?

Back

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

Front

What is the meaning of the inequality x < -5?

Back

It means that x can be any number less than -5.

Front

Joanna needs to make at least $100. What inequality represents her earnings?

Back

60 + 5x ≥ 100, where x is the number of items sold.

Front

How do you solve the inequality 22 < 6c + 4?

Back

Subtract 4 from both sides: 18 < 6c. Then divide by 6: 3 < c or c > 3.

Front

What does the solution c > 3 indicate?

Back

It indicates that c can be any number greater than 3.

Front

How do you solve the inequality 2 - 3x ≤ 20?

Back

Subtract 2 from both sides: -3x ≤ 18. Then divide by -3 (flip the inequality): x ≥ -6.

Front

What does the solution x ≥ -6 mean?

Back

It means that x can be any number greater than or equal to -6.