Solving Two-Step Inequalities

You flip an inequality symbol when you...

• subtract

• multiply and divide by any number

• subtract or multiple by a negative number

• multiple or divide by a negative number

Solve and graph.
k - 13 > -51

• A

• B

• C

• D

Solve and graph the inequality.
7n - 1 > 76

• A

• B

• C

• D

Solve the following inequality for x:

2.5x + 3.75 ≤ 16.25

• x ≤ 5

• x ≥ 5

• x ≤ 8

• x ≥ 8

25 < X - 10

• X > 35

• X < 35

• X > -35

• X < -35

Solve for t.

6t + 4 ≤ 22

• t ≤ -3

• t ≤ 3

• t ≥ -3

• t ≥ 3

Daniel can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?

• 10x + 1.50 ≥ 40

• 1.50x + 10 ≤ 40

• 1.50x + 10 <40

• 10x + 1.50 < 40

Nick had $26.50 to spend at the fair. Admission to the fair was $8.50 and rides cost $1.50 per ticket. Which inequality and solution represents how many ride tickets Nick can purchase?

• 8.50 + 1.50x < 26.50; Nick can purchase more than 12 tickets

• 8.50 + 1.50x > 26.50; Nick can purchase more than 12 tickets

• 8.50 + 1.50x ≤ 26.50; Nick can purchase no more than 12 tickets

• 8.50 + 1.50x ≥ 26.50; Nick can purchase no more than 12 tickets

2- 3x ≤ 20

• x  ≥ -6
• x ≤ -6
• x ≤ -7
• x  ≥ -7

Nick has $7.00. Bagels cost $0.75 each, and a small container of cream cheese costs $1.29. Write an inequality to find the numbers of bagels Nick can buy. Identify what your variable represents.

• 0.75 + 1.29N < 7.00; n = the number of bagels Nick can buy

• 0.75n + 1.29 < 7.00; n = the number of bagels Nick can buy

• 0.75n - 1.29 < 7.00; n = the number cream cheese Nick can buy

• 0.75 - 1.29n > 7.00; n = the number of bagels Nick can buy