1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up Solve. 1. 6x + 36 = 2x 2. 4x – 13 = 15 + 5x7 8 13 1 16
x = – 16

3. Find an integer x that makes the following two inequalities true:
Problem of the Day
Find an integer x that makes the following two inequalities true:
4 < x2 < 16 and x < 2.5
x = –3

4. Learn to solve multistep inequalities and graph the solutions of an inequality on a number line.

5. Additional Example 1A: Solving Two-Step Inequalities
Solve and graph.
4x + 1 > 13
4x + 1 > 13
– 1 – 1 Subtract 1 from both sides.
4x > 12 4x 4
> 12
Divide both sides by 4.
x > 3

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

7. Additional Example 1B: Solving Two-Step Inequalities
Solve 2(x + 4) – 11x  26 and graph.
2(x + 4) – 11x  26
Distributive Property
2x + 8 – 11x  26
–9x + 8  26
Simplify.
– 8 – Subtract 8 from both sides.
–9x  18
–9x –9  18
Divide each side by –9; change  to .
x  –2

8. – 2 – 2 Subtract 2 from both sides.
Check It Out: Example 1A
Solve and graph.
5x + 2 > 12
5x + 2 > 12
– 2 – 2 Subtract 2 from both sides.
5x > 10 5x 5
> 10
Divide both sides by 5.
x > 2

9. – 2 – 2 Subtract 2 from both sides.
Check It Out: Example 1B
–4x + 2  18
–4x + 2  18
– 2 – 2 Subtract 2 from both sides.
–4x  16
–4x –4  16
Divide each side by –4; change  to .
x  –4

10. Additional Example 2: Solving Inequalities That Contain Fractions5 3 4 9 10
Solve  and graph the solution.
+  2x 5 3 4 9 10
20( + )  20( ) 2x 5 3 4 9 10
Multiply by LCD, 20.
20( ) + 20( )  20( ) 2x 5 3 4 9 10
Distributive Property.
8x + 15  18
– 15 – Subtract 15 from both sides.
8x  3

11. Additional Example 2 Continued 8x 8 3
Divide both sides by 8.
x  3 8 3 8

12. Check It Out: Example 2
Solve  3x 5 1 4 10
+  3x 5 1 4 10
20( + )  20( ) 3x 5 1 4 10
Multiply by LCD, 20.
20( ) + 20( )  20 ( ) 3x 5 1 4 10
Distributive Property.
12x + 5  10
– 5 – Subtract 5 from both sides.
12x  5

13. Check It Out: Example 2 Continued
12x 12 5
Divide both sides by 12.
x  5 12 5 12

14. 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?
Let R represent the revenue and C represent the cost. In order for the Spanish club to make a profit, the revenue must be greater than the cost.
R > C

15. Additional Example 3 Continued
The revenue from selling x bumper stickers at $1.25 each is 1.25x. The cost of selling x bumper stickers is the fixed cost plus the unit cost times the number of bumper stickers sold, or x. Substitute the expressions for R and C.
1.25x > x
Let x represent the number of bumper stickers sold. Fixed cost is $55. Unit cost is 15 cents.

16. Additional Example 3 Continued
1.25x > x
Subtract 0.15x from both sides.
– 0.15x – 0.15x
1.10x > 55
1.10x
1.10 55
>
Divide both sides by 1.10.
x > 50
The Spanish club must sell more than 50 bumper stickers to make a profit.

17. 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?
Let R represent the revenue and C represent the cost. In order for the French club to make a profit, the revenue must be greater than the cost.
R > C

18. Check It Out: Example 3 Continued
The revenue from selling x bumper stickers at $2.50 each is 2.5x. The cost of selling x bumper stickers is the fixed cost plus the unit cost times the number of bumper stickers sold, or x. Substitute the expressions for R and C.
2.5x > x
Let x represent the number of bumper stickers sold. Fixed cost is $45. Unit cost is 25 cents.

19. Check It Out: Example 3 Continued
2.5x > x
Subtract 0.25x from both sides.
– 0.25x – 0.25x
2.25x > 45
2.25x
2.25 45
>
Divide both sides by 2.25.
x > 20
The French club must sell more than 20 bumper stickers to make a profit.

20. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

21. Lesson Quiz: Part I Solve and graph. 1. 4x – 6 > 10
2. 7x + 9 < 3x – 15
3. w – 3w < 32
4. w + 
x > 4
x < –6
w > –16 2 3 1 4 1 2
w  3 8 3 8

22. 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

23. Lesson Quiz for Student Response Systems
1. Solve and identify the graph of the inequality.
6x – 5 > 13
A. x > 3
B. x > –3
C. x < 3
D. x < –3

24. Lesson Quiz for Student Response Systems
2. Solve and identify the graph of the inequality.
11x + 15 > 4x – 20
A. x > 5
B. x < 5
C. x > –5
D. x < –5

25. Lesson Quiz for Student Response Systems
3. Adam planned to save for 10 months to buy a DVD player that costs $500. He was able to save $242 in four months. How much should he save per month for the next six months?
A. at least $43
B. at least $45
C. no more than $43
D. no more than $45