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Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
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Warm Up Solve. 1. 6x + 36 = 2x 2. 4x – 13 = 15 + 5x
7 8 13 1 16 x = – 16
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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
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Learn to solve multistep inequalities and graph the solutions of an inequality on a number line.
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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
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If both sides of an inequality are multiplied or divided by a negative number, the inequality symbol must be reversed. Remember!
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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
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– 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
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– 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
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Additional Example 2: Solving Inequalities That Contain Fractions
5 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
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Additional Example 2 Continued
8x 8 3 Divide both sides by 8. x 3 8 3 8
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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
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Check It Out: Example 2 Continued
12x 12 5 Divide both sides by 12. x 5 12 5 12
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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
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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.
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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.
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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
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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.
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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.
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Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems
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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
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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
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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
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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
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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
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