Holt Algebra 1

3-4Solving Two-Step and Multi-Step Inequalities

Warm UpSolve each equation. 1. 2x – 5 = –17

2.

Solve each inequality and graph the solutions.

4.

3. 5 < t + 9

–6

14

t > –4

a ≤ –8

Holt Algebra 1

3-4Solving Two-Step and Multi-Step Inequalities

Students will be able to: Solve inequalities that contain more than one operation.

Learning Target

Holt Algebra 1

3-4Solving Two-Step and Multi-Step Inequalities

Solve the inequality and graph the solutions.

45 + 2b > 61

–10 –8 –6 –4 –2 0 2 4 6 8 10

45452 16b

22

8b 8 – 3y ≥ 29

–10 –8 –6 –4 –2 0 2 4 6 8 1088

3 21y 337y

Holt Algebra 1

3-4Solving Two-Step and Multi-Step Inequalities

11x

5 6x

Solve the inequality and graph the solutions.

2 2

55 1113 9

3 3

1 2 21n 11

2 20n 2210n

–10 –8 –6 –4 –2 0 2 4 6 8 10

Holt Algebra 1

3-4Solving Two-Step and Multi-Step Inequalities

Solve the inequality and graph the solutions.

2 – (–10) > –4t

–10 –8 –6 –4 –2 0 2 4 6 8 10

2 10 4t 12 4t

443 t

Holt Algebra 1

3-4Solving Two-Step and Multi-Step Inequalities

4 16x

8 4 8x

Solve the inequality and graph the solutions.

–4(2 – x) ≤ 8

–10 –8 –6 –4 –2 0 2 4 6 8 1088

444x

Holt Algebra 1

3-4Solving Two-Step and Multi-Step Inequalities

4 1f

4 3 2f

Solve the inequality and graph the solutions.

–10 –8 –6 –4 –2 0 2 4 6 8 10

[ ]6

33

44

1

4f

1

4

Holt Algebra 1

3-4Solving Two-Step and Multi-Step Inequalities

2 20m

Solve the inequality and graph the solutions.

2m + 5 > 52

–10 –8 –6 –4 –2 0 2 4 6 8 10

2 5 25m 55

2210m

Holt Algebra 1

3-4Solving Two-Step and Multi-Step Inequalities

17 0.20M

55 38 0.20M

To rent a certain vehicle, Rent-A-Ride charges $55.00 per day with unlimited miles. The cost of renting a similar vehicle at We Got Wheels is $38.00 per day plus $0.20 per mile. For what number of miles is the cost at Rent-A-Ride less than the cost at We Got Wheels?

Rent-A-Ride costs less when the number of miles is more than 85.

3838

0.200.20 85M

Holt Algebra 1

3-4Solving Two-Step and Multi-Step Inequalities

9590

2

x

The average of Jim’s two test scores must be at least 90 to make an A in the class. Jim got a 95 on his first test. What grades can Jim get on his second test to make an A in the class?

The score on the second test must be 85 or higher.

x ≥ 85HW pp.191-193/16-37,38 

1 2 902

t t

2 2

95 180x

Holt Algebra 1

3-4Solving Two-Step and Multi-Step Inequalities

Solve 18 = 4a + 10

5t – 2 = –32

–4 + 7x = 3

1.5 = 1.2y – 5.7

10108 4a

4421

2 a

225 30t 5 5

6t

447 7x 7 7

1x 5.75.7

7.2 1.2y1.2 1.2

6 y