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 -3x + 14 ≤ 44?

Back

Subtract 14 from both sides: -3x ≤ 30. Then divide by -3 (remember to flip the inequality): x ≥ -10.

Front

What does the solution x ≥ -10 mean in a real-world context?

Back

It means that the value of x can be any number greater than or equal to -10.

Front

How do you solve the inequality 2x + 3 ≤ 15?

Back

Subtract 3 from both sides: 2x ≤ 12. Then divide by 2: x ≤ 6.

Front

What does the solution x ≤ 6 indicate?

Back

It indicates that x can be any number less than or equal to 6.

Front

In the context of Nick's tutoring, how do you set up the inequality for his earnings?

Back

The inequality is 60 + 15h ≥ 120, where h is the number of hours he tutors.

Front

How do you solve the inequality for Nick's tutoring hours?

Back

Subtract 60 from both sides: 15h ≥ 60. Then divide by 15: h ≥ 4.

Front

What does h ≥ 4 signify for Nick's situation?

Back

It means Nick needs to tutor at least 4 hours to have enough money for the shoes.

Front

How do you set up the inequality for Molly's bowling budget?

Back

The inequality is 42 - 10 - 8g ≥ 0, where g is the number of games.

Front

How do you solve the inequality for the number of games Molly can bowl?

Back

Rearranging gives: 8g ≤ 32, then divide by 8: g ≤ 4.