Solve Two-Step Inequalities Lesson Check

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 5x + 9 > 34?

Back

Subtract 9 from both sides: 5x > 25. Then divide by 5: x > 5.

Front

What does the solution x > 5 represent on a number line?

Back

It represents all numbers greater than 5, which is shown as an open circle at 5 and a line extending to the right.

Front

How do you solve the inequality -2x - 3 ≤ 13?

Back

Add 3 to both sides: -2x ≤ 16. Then divide by -2 (remember to flip the inequality): x ≥ -8.

Front

What does the solution x ≥ -8 mean?

Back

It means x can be -8 or any number greater than -8, represented by a closed circle at -8 and a line extending to the right.

Front

How do you graph the inequality 77 ≤ 5 + 8n?

Back

First, solve for n: 8n ≥ 72, so n ≥ 9. Graph with a closed circle at 9 and a line extending to the right.

Front

What is the solution to the inequality -3r + 10 < -2?

Back

Subtract 10 from both sides: -3r < -12. Then divide by -3 (flip the inequality): r > 4.

Front

What does the solution r > 4 indicate?

Back

It indicates that r can be any number greater than 4, shown with an open circle at 4 and a line extending to the right.

Front

How do you solve the inequality 7b - 3 < 11?

Back

Add 3 to both sides: 7b < 14. Then divide by 7: b < 2.

Front

What does the solution b < 2 signify?

Back

It signifies that b can be any number less than 2, represented by an open circle at 2 and a line extending to the left.