HW # 78 - p. 150 & 151 # 1-54 even

Warm up

Week 23, Day Three

Solve. Graph the solution.

1. 6x + 36 = 2x

2. 4x – 13 = 15 + 5x

3. 5(x – 3) = 2x + 3

4. + x =

x = –9

x = –28

x = 678

1316

1 16x = –

You need to do your audit TODAY!

Warm Up Response ~$

Homework Checkp. 146 & 147 # 1-44 even

Goals for Today

• 3-8 Solving Two-Step Inequalities • Examples and Notes from p. 148 & 149 • CW: Inequalities Worksheet A

Extra slides for practice

When you solved two-step equations, you used the order of operations in reverse to isolate the variable. You can use the same process when solving two-step inequalities.

Solve and graph.

Additional Example 1A: Solving Two-Step Inequalities

4x + 1 > 13

4x + 1 > 13 – 1 – 1 Since 1 is added to 4x, subtract 1 from both sides. 4x > 12

4x4

> 124

Since x is multiplied by 4, divide both sides by 4.

x > 3

1 2 3 4 5 6 7

Additional Example 1A Continued

Check

x > 3

4 > 3?Substitute 4 for x.

According to the graph 4 should be a solution and 2 should not be a solution.

So 4 is a solution.

x > 3

2 > 3?Substitute 2 for x.

So 2 is not a solution.

If both sides of an inequality are multiplied or divided by a negative number, the inequality symbol must be reversed.

Remember!

Additional Example 1B: Solving Two-Step Inequalities

–9x + 7 25

–9x + 7 25

– 7 – 7 Subtract 7 from both sides.

–9x 18

–9x–9

18–9

Divide each side by –9; change to .

x –2-6 -5 -4 -3 -2 -1 0

Solve and graph.

Solve and graph.

Check It Out! Example 1A

5x + 2 > 12

5x + 2 > 12 – 2 – 2 Subtract 2 from both sides. 5x > 10

5x5

> 105

Divide both sides by 5.

x > 2 1 2 3 4 5 6 7

Check It Out! Example 1A Continued

Check

x > 2

4 > 2?Substitute 4 for x.

According to the graph 4 should be a solution and 1 should not be a solution.

So 4 is a solution.

x > 2

1 > 2?Substitute 1 for x.

So 1 is not a solution.

–4x + 2 18

–4x + 2 18

– 2 – 2 Subtract 2 from both sides.

–4x 16

–4x–4

16–4

Divide each side by –4; change to .

x –4-6 -5 -4 -3 -2 -1 0

Check It Out! Example 1B

Additional Example 3: School Application

A school’s Spanish club is selling bumper stickers. They bought 100 bumper stickers for $55, and they have to give the company 15 cents for every sticker sold. If they plan to sell each bumper sticker for $1.25, how many do they have to sell to make a profit?

In order for the Spanish club to make a profit, the revenue must be greater than the cost.

1.25x > 55 + 0.15x

Additional Example 3 Continued

– 0.15x – 0.15x Subtract 0.15x from both sides.

1.10x > 55

x > 50

The Spanish club must sell more than 50 bumper stickers to make a profit.

Divide both sides by 1.10.

1.25x > 55 + 0.15x

1.10x1.10

551.10>

Check It Out! Example 3

A school’s French club is selling bumper stickers. They bought 200 bumper stickers for $45, and they have to give the company 25 cents for every sticker sold. If they plan to sell each bumper sticker for $2.50, how many do they have to sell to make a profit?

In order for the French club to make a profit, the revenue must be greater than the cost.

2.5x > 45 + 0.25x

– 0.25x – 0.25x Subtract 0.25x from both sides.

2.25x > 45

x > 20

The French club must sell more than 20 bumper stickers to make a profit.

Divide both sides by 2.25.

2.5x > 45 + 0.25x

2.25x2.25

452.25>

Check It Out! Example 3 Continued

Lesson Quiz: Part I

Solve and graph.

1. 4x – 6 > 10

2. 7x + 9 < 3x – 15

3. w – 3w < 32

4. w +

x < –6

x > 4

w > –1623

14

12

w 38

1 2 3 4 5 6 7

-10 -9 -8 -7 -6 -5 -4

-18 -17 -16 -15 -14 -13 -12

0 38

Lesson Quiz: Part II

5. Antonio has budgeted an average of $45 a month for entertainment. For the first five months of the year he has spent $48, $39, $60, $48, and $33. How much can Antonio spend in the sixth month without exceeding his average budget?

no more than $42