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Warm Up Solve. 1. 2 x + 8 = x – 7 2. –4( x + 3) = –5 x – 2

Warm Up Solve. 1. 2 x + 8 = x – 7 2. –4( x + 3) = –5 x – 2 3. 5 x + x + ( - 11) = 25 – 3 x 4. 6 n + 9 – 4 n = 3 n. x = –15. x = 10. x = 4. n = 9.

sydney-munoz
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Warm Up Solve. 1. 2 x + 8 = x – 7 2. –4( x + 3) = –5 x – 2

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  1. Warm Up Solve. 1. 2x + 8 = x – 7 2. –4(x + 3) = –5x – 2 3. 5x + x + (-11) = 25 – 3x 4. 6n + 9 – 4n = 3n x = –15 x = 10 x = 4 n = 9

  2. The steps for solving inequalities by multiplying or dividing are the same as for solving equations, with one exception. If both sides of an inequality are multiplied or divided by a negative number, the inequality symbol must be reversed.

  3. Remember! When graphing an inequality on a number line, an open circle means that the point is not part of the solution and a closed circle means that the point is part of the solution.

  4. a 4 4• 12 < 4 • Example 1 Solve and graph. a 4 12 < Multiply both sides by 4. 48 < a, or a > 48 43 44 45 46 47 48 49 50 51 52 53 54

  5. 12 < 12.25 12 < 12 < 12 < 11.75 12 < 12 < a 4 a 4 49 4 47 4 ? ? ? ? Example 1 Continued Check According to the graph, 49 should be a solution because 49 > 48, and 47 should not be a solution because 47 < 48. Substitute 49 for a. Substitute 47 for a. x So 49 is a solution. So 47 is not a solution.

  6. 45-9 -9b-9 ≥ Example 2 Solve and graph. –9b ≤ 45 Divide both sides by -9; ≤ changes to ≥. b ≥ -5 0 –5

  7. –4a–4 12–4 ≥ Example 3 Solve and graph. 12 ≤ –4a Divide both sides by -4; ≤ changes to ≥. -3 ≥ a 0 –3

  8. x q 3 8 Lesson Quiz: Part I Solve and graph. 1. –14x > 28 x<–2 2. < 15 x< 45 3. 18< –6x –3 > x 4. 5 q ≥ 40

  9. Problem Solving Application A rock-collecting club needs to make at least $500. They are buying rocks for $2.50 and selling them for $4.00. What is the least number of rocks the club must sell to make their goal?

  10. 1 Understand the Problem rocks bought $ rocks sold $ # of rocks needed to sell to make $500. - • ≥ $500 Problem Solving Continued The answer is the least number of rocks the club must sell to make their goal. List the important information: • The club needs to make at least $500. • The club is buying rocks for $2.50. • The club is selling rocks for $4.00. Show the relationship of the information:

  11. Make a Plan r - • ≥ 2.50 $500 4.00 2 Problem Solving Continued Use the information to write an inequality. Let r represent the number of rocks needed to be sold in order for the club to make at least $500.

  12. 3 Solve 1.50r ≥ 500 1.501.50 Problem Solving Continued (4.00 – 2.50) • r ≥ 500 Simplify. 1.50r ≥ 500 Divide both sides by 1.50. r ≥ 333.33… 334 rocks need to be sold in order for the club to make at least $500.

  13. 4 Problem Solving Continued Look Back Since the rock-collecting club is reselling rocks, they are making a $1.50 profit from each rock. $1.50(334) ≥ $500, or $501 ≥ $500.

  14. Problem Solving 2 The music club needs to make at least 3 times more than the language club made ($132) in order to go to the symphony. They are selling music sheet holders for $3.75. What is the number of music sheet holders the club must sell to make their goal?

  15. 1 Understand the Problem Problem Solving 2 The answer is the least number of music sheet holders the club must sell to make their goal. List the important information: • The club needs to make at least three times the amount of the language club ($132). • The club is selling music sheet holders for $3.75. Show the relationship of the information: amount($) music holders sold for. # of holders needed to sell. • ≥ 3 • $132

  16. Make a Plan 2 Problem Solving 2 Continued Use the information to write an inequality. Let m represent the number of music sheet holders needed to be sold in order for the club to make at least three times the amount of the language club. m $3.75 • ≥ 3 • $132

  17. 3 Solve 3.75m ≥ 396 3.753.75 Problem Solving 2 Continued 3.75 • m ≥ 3 • 132 Simplify. 3.75m ≥ 396 Divide both sides by 3.75. m ≥ 105.6 106 music sheet holders need to be sold in order for the club to make at least three times the amount of the language club or $396.

  18. For the music club to make as much money as the language club they would need to sell or 35.2 music sheet holders. In order to make three times the amount it would take 3(35.2) or 106 • $3.75 = $398 ≥ $396. 132 3.75 4 Problem Solving 2 Continued Look Back

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