page 510 #10-20 answers. pre-algebra 10-4 solving multistep inequalities student progress chart...

#10-20 ANSWERS

Pre-Algebra

10-4 Solving Multistep Inequalities

Student Progress Chart

Lesson Reflection

Pre-Algebra


Pre-Algebra


Today’s Learning Goal Assignment

Learn to solve two-step inequalities and graph the solutions of an inequality on a number line.

Pre-Algebra



17#14-26

Solve & Graph!

Pre-Algebra

10-4 Solving Multistep Inequalities10-4 Solving Multistep Inequalities

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra


Warm UpSolve.

1. 6x + 36 = 2x

2. 4x – 13 = 15 + 5x

3. 5(x – 3) = 2x + 3

4. + x =

x = –9

x = –28

x = 6

Pre-Algebra


78

316

1116

x = –

Pre-Algebra


Problem of the Day

Find an integer x that makes the following two inequalities true:4 < x2 < 16 and x < 2.5

x = –3

Pre-Algebra



Learn to solve two-step inequalities and graph the solutions of an inequality on a number line.

Pre-Algebra


Solving a multistep inequality uses the same inverse operations as solving a multistep equation. Multiplying or dividing the inequality by a negative number reverses the inequality symbol.

Pre-Algebra


Solve and graph.

Additional Example 1A: Solving Multistep Inequalities

A. 4x + 1 > 13

4x + 1 > 13 – 1 – 1 Subtract 1 from both sides.

4x > 124x4

> 124

Divide both sides by 4.

x > 3 1 2 3 4 5 6 7

Pre-Algebra


Additional Example 1B: Solving Multistep Inequalities

B. –7 < 3x + 8

–7 < 3x + 8

– 8 – 8 Subtract 8 from both sides.

–15 < 3x

– 15 3

< 3x 3 Divide both sides by 3.

–5 < x -7 -6 -5 -4 -3 -2 -1

Pre-Algebra


Additional Example 1C: Solving Multistep Inequalities

C. -9x + 7 25

–9x + 7 25


–9x 18

–9x–9

18–9

Divide each side by –9; change to .

x –2-6 -5 -4 -3 -2 -1 0

Pre-Algebra


Solve and graph.

Try This: Example 1A

A. 5x + 2 > 12

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

5x > 105x5

> 105


x > 2 1 2 3 4 5 6 7

Pre-Algebra


B. –5 < 2x + 9

–5 < 2x + 9


–14 < 2x

– 14 2

< 2x 2 Divide both sides by 2.

–7 < x -7 -6 -5 -4 -3 -2 -1

Try This: Example 1B

Pre-Algebra


C. -4x + 2 18

–4x + 2 18


–4x 16

–4x–4

16–4

Divide each side by –4; change to .

x –4-6 -5 -4 -3 -2 -1 0

Try This: Example 1C

Pre-Algebra


Solve and graph.

Additional Example 2A: Solving Multistep Inequalities

A. 10x + 21 – 4x < –15

10x + 21 – 4x < –15


6x6

< –36 6 Divide both sides by 6.

x < –6-8 -7 -6 -5 -4 -3 -2

6x + 21 < –15 Combine like terms.

6x < –36

Pre-Algebra


Additional Example 2B: Solving Multistep Inequalities

Multiply by LCD, 20.

8x + 15 18


8x 3

B. + 2x5

34

910

+ 2x5

34

910

20( + ) 20( )2x5

34

910

20( ) + 20( ) 20( )2x5

34

910

Pre-Algebra


Additional Example 2 Continued

x 38

8x8

38 Divide both sides by 8.

8x 3

0 1

38

Pre-Algebra


Additional Example 2C: Solving Multistep Inequalities

C. 8x + 8 > 11x – 1

8x + 8 > 11x – 1– 8x – 8x Subtract 8x from both sides.

8 > 3x – 1

93

> 3x 3

Add 1 to each side.

3 > x

-1 0 1 2 3 4 5

+1 +1

9 > 3x


Pre-Algebra


Solve and graph.

Try This: Example 2A

A. 15x + 30 – 5x < –10

15x + 30 – 5x < –10


10x10

< –40 10 Divide both sides by 10.

x < –4-8 -7 -6 -5 -4 -3 -2

10x + 30 < –10 Combine like terms.

10x < –40

Pre-Algebra


Try This: Example 2B

Multiply by LCD, 20.

12x + 5 10


12x 5

B. + 3x5

14

510

+ 3x5

14

510

20( + ) 20( )3x5

14

510

20( ) + 20( ) 20 ( )3x5

14

510

Pre-Algebra


Try This: Example 2B Continued

x 512

12x12

512 Divide both sides by 12.

12x 5

0 5 12

Pre-Algebra


Try This: Example 2C

C. 4x + 3 > 8x – 1

4x + 3 > 8x – 1– 4x – 4x Subtract 4x from both sides.

3 > 4x – 1

44

> 4x 4

Add 1 to each side.

1 > x

-1 0 1 2 3 4 5

+1 +1

4 > 4x


Pre-Algebra


Additional Example 3: Business 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

Pre-Algebra



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 55 + 0.15x. Substitute the expressions for R and C.

1.25x > 55 + 0.15x Let x represent the number of bumper stickers sold. Fixed cost is $55. Unit cost is 15 cents.

Pre-Algebra



– 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>

Pre-Algebra


Try This: Example 3

R > C

A school’s Spanish 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 Spanish club to make a profit, the revenue must be greater than the cost.

Pre-Algebra


Try This: 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 45 + 0.25x. Substitute the expressions for R and C.

2.5x > 45 + 0.25x Let x represent the number of bumper stickers sold. Fixed cost is $45. Unit cost is 25 cents.

Pre-Algebra


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

2.25x > 45

x > 20

The Spanish 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>

Try This: Example 3 Continued

Pre-Algebra


Lesson Quiz: Part 1

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

Pre-Algebra


Lesson Quiz: Part 2

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 1 can Antonio spend in the sixth month without exceeding his average budget?

no more than $42

page 510 #10-20 answers. pre-algebra 10-4 solving multistep inequalities student progress chart...

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