lesson 9.8 solving two-step inequalities · 2013-10-13 · solving multi-step inequalities solve...

Warm Up

Solve 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

Solve inequalities that contain more than one

operation

Inequalities that contain more than one

operation require more than one step to solve.

Use inverse operations to undo the operations

in the inequality one at a time.

Step 1: Undo addition or subtraction

Step 2: Undo multiplication and division

Is your variable isolated?

Subtracting a number is the same as adding its

opposite.

7 – 2t = 7 + (–2t)

Remember!

Solving Multi-Step Inequalities

Solve the inequality and graph the solutions.

45 + 2b > 61

45 + 2b > 61

–45 –45

2b > 16

b > 8

0 2 4 6 8 10 12 14 16 18 20

1. Add/ Subtract

2. Multiply/Divide

The solution set is {b:b > 8}.

8 – 3y ≥ 29

8 – 3y ≥ 29

–8 –8

–3y ≥ 21

y ≤ –7

1. Add/Subtract

2. Multiply/Divide

–10 –8 –6 –4 –2 0 2 4 6 8 10

–7

Solving Multi-Step Inequalities

Solve the inequality and graph the solutions.

The solution set is {y:y –7}.

Solve and Graph the inequality

1)9 2b13

2)2x 13 9

3)y

512 8

4) 3m 5 17

To solve more complicated inequalities, you

may first need to simplify the expressions on

one or both sides.

Simplifying Before Solving Inequalities

Solve the inequality and graph the solutions.

2 – (–10) > –4t

–10 –8 –6 –4 –2 0 2 4 6 8 10

Simplifying Before Solving Inequalities

Solve the inequality and graph the solutions.

–4(2 – x) ≤ 8

–10 –8 –6 –4 –2 0 2 4 6 8 10

Now you try…

x > 3

x ≥ -1

x ≤ 2

x < 35

x ≥ -27

1. 3x – 7 > 2 4. x – 4 < 3

5

2. 4x + 1 -3

5. 15 + x ≥ 6

3

3. 2x – 7 ≤ -3

Lesson Quiz: Part I

Solve each inequality and graph the solutions.

1. 13 – 2x ≥ 21 x ≤ –4

2. –11 + 2 < 3p p > –3

3. 23 < –2(3 – t) t > 7

4.

Lesson Quiz: Part II

5. A video store has two movie rental plans. Plan A

includes a $25 membership fee plus $1.25 for each

movie rental. Plan B costs $40 for unlimited movie

rentals. For what number of movie rentals is plan B

less than plan A?

more than 12 movies