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10 -4 Solving Multistep Inequalities Student Progress Chart Lesson Reflection Pre-Algebra

10 -4 Solving Multistep Inequalities Pre-Algebra

10 -4 Solving Multistep Inequalities Today’s Learning Goal Assignment Learn to solve twostep inequalities and graph the solutions of an inequality on a number line. Pre-Algebra

10 -4 Solving Multistep Inequalities Today’s Learning Goal Assignment Page 517 #14 -26 Solve & Graph! Pre-Algebra

10 -4 Solving. Multistep. Inequalities Warm Up Problem of the Day Lesson Presentation Pre-Algebra

10 -4 Solving Multistep Inequalities Warm Up Solve. 1. 6 x + 36 = 2 x x = – 9 2. 4 x – 13 = 15 + 5 x x = – 28 3. 5(x – 3) = 2 x + 3 3 4. 7 + x = 16 8 Pre-Algebra x=6 x = – 11 16

10 -4 Solving Multistep Inequalities Problem of the Day Find an integer x that makes the following two inequalities true: 4 < x 2 < 16 and x < 2. 5 x = – 3 Pre-Algebra

10 -4 Solving Multistep Inequalities Today’s Learning Goal Assignment Learn to solve twostep inequalities and graph the solutions of an inequality on a number line. Pre-Algebra

10 -4 Solving Multistep Inequalities 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

10 -4 Solving Multistep Inequalities Additional Example 1 A: Solving Multistep Inequalities Solve and graph. A. 4 x + 1 > 13 – 1 4 x > 12 4 x> 12 4 4 x>3 Pre-Algebra Subtract 1 from both sides. Divide both sides by 4. 1 2 3 4 5 6 7

10 -4 Solving Multistep Inequalities Additional Example 1 B: Solving Multistep Inequalities B. – 7 < 3 x + 8 – 8 Subtract 8 from both sides. – 15 < 3 x 3 3 – 5 < x Pre-Algebra Divide both sides by 3. -7 -6 -5 -4 -3 -2 -1

10 -4 Solving Multistep Inequalities Additional Example 1 C: Solving Multistep Inequalities C. -9 x + 7 25 – 7 – 9 x – 7 Subtract 7 from both sides. 18 – 9 x 18 – 9 x – 2 Pre-Algebra Divide each side by – 9; change to . -6 -5 -4 -3 -2 -1 0

10 -4 Solving Multistep Inequalities Try This: Example 1 A Solve and graph. A. 5 x + 2 > 12 – 2 5 x > 10 5 x> 10 5 5 x>2 Pre-Algebra Subtract 2 from both sides. Divide both sides by 5. 1 2 3 4 5 6 7

10 -4 Solving Multistep Inequalities Try This: Example 1 B B. – 5 < 2 x + 9 – 9 Subtract 9 from both sides. – 14 < 2 x 2 2 – 7 < x Pre-Algebra Divide both sides by 2. -7 -6 -5 -4 -3 -2 -1

10 -4 Solving Multistep Inequalities Try This: Example 1 C C. -4 x + 2 18 – 2 – 4 x – 2 Subtract 2 from both sides. 16 – 4 x 16 – 4 x – 4 Pre-Algebra Divide each side by – 4; change to . -6 -5 -4 -3 -2 -1 0

10 -4 Solving Multistep Inequalities Additional Example 2 A: Solving Multistep Inequalities Solve and graph. A. 10 x + 21 – 4 x < – 15 6 x + 21 – 21 6 x < – 15 Combine like terms. – 21 Subtract 21 from both sides. < – 36 6 x< – 36 Divide both sides by 6. 6 6 x < – 6 -8 Pre-Algebra -7 -6 -5 -4 -3 -2

10 -4 Solving Multistep Inequalities Additional Example 2 B: Solving Multistep Inequalities B. 2 x + 3 9 5 4 10 9 Multiply by LCD, 20. 2 x 3 20 5 + 4 20 10 3 9 2 x 20 5 + 20 4 20 10 8 x + 15 18 ( () ) () () () – 15 8 x 3 Pre-Algebra Subtract 15 from both sides.

10 -4 Solving Multistep Inequalities Additional Example 2 Continued 8 x 3 8 8 Divide both sides by 8. x 3 8 0 Pre-Algebra 3 8 1

10 -4 Solving Multistep Inequalities Additional Example 2 C: Solving Multistep Inequalities C. 8 x + 8 > 11 x – 1 – 8 x 8 > 3 x – 1 +1 +1 9 > 3 x 3 3 3>x Subtract 8 x from both sides. Add 1 to each side. Divide both sides by 3. -1 Pre-Algebra 0 1 2 3 4 5

10 -4 Solving Multistep Inequalities Try This: Example 2 A Solve and graph. A. 15 x + 30 – 5 x < – 10 10 x + 30 – 30 10 x < – 10 Combine like terms. – 30 Subtract 30 from both sides. < – 40 10 x < – 40 10 10 Divide both sides by 10. x < – 4 -8 Pre-Algebra -7 -6 -5 -4 -3 -2

10 -4 Solving Multistep Inequalities Try This: Example 2 B B. 3 x + 1 5 5 4 10 5 Multiply by LCD, 20. 3 x 1 20 5 + 4 20 10 1 5 3 x 20 5 + 20 4 20 10 12 x + 5 10 ( () ) () () () – 5 12 x 5 Pre-Algebra Subtract 5 from both sides.

10 -4 Solving Multistep Inequalities Try This: Example 2 B Continued 12 x 5 12 12 Divide both sides by 12. x 5 12 0 Pre-Algebra 5 12

10 -4 Solving Multistep Inequalities Try This: Example 2 C C. 4 x + 3 > 8 x – 1 – 4 x 3 > 4 x – 1 +1 +1 4 > 4 x 4 4 1>x Subtract 4 x from both sides. Add 1 to each side. Divide both sides by 4. -1 Pre-Algebra 0 1 2 3 4 5

10 -4 Solving Multistep Inequalities 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

10 -4 Solving Multistep Inequalities Additional Example 3 Continued The revenue from selling x bumper stickers at $1. 25 each is 1. 25 x. 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. 15 x. Substitute the expressions for R and C. 1. 25 x > 55 + 0. 15 x Pre-Algebra Let x represent the number of bumper stickers sold. Fixed cost is $55. Unit cost is 15 cents.

10 -4 Solving Multistep Inequalities Additional Example 3 Continued 1. 25 x > 55 + 0. 15 x – 0. 15 x 1. 10 x > 55 1. 10 x 55 > 1. 10 Subtract 0. 15 x from both sides. Divide both sides by 1. 10. x > 50 The Spanish club must sell more than 50 bumper stickers to make a profit. Pre-Algebra

10 -4 Solving Multistep Inequalities Try This: Example 3 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. R>C Pre-Algebra

10 -4 Solving Multistep Inequalities Try This: Example 3 Continued The revenue from selling x bumper stickers at $2. 50 each is 2. 5 x. 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. 25 x. Substitute the expressions for R and C. 2. 5 x > 45 + 0. 25 x Pre-Algebra Let x represent the number of bumper stickers sold. Fixed cost is $45. Unit cost is 25 cents.

10 -4 Solving Multistep Inequalities Try This: Example 3 Continued 2. 5 x > 45 + 0. 25 x – 0. 25 x 2. 25 x > 45 2. 25 x 45 > 2. 25 Subtract 0. 25 x from both sides. Divide both sides by 2. 25. x > 20 The Spanish club must sell more than 20 bumper stickers to make a profit. Pre-Algebra

10 -4 Solving Multistep Inequalities Lesson Quiz: Part 1 Solve and graph. 1. 4 x – 6 > 10 x>4 2. 7 x + 9 < 3 x – 15 x < – 6 3. w – 3 w < 32 w > – 16 4. 2 w + 1 1 4 3 3 w 8 Pre-Algebra 2 1 2 3 4 5 6 7 -10 -9 -8 -7 -6 -5 -4 -18 -17 -16 -15 -14 -13 -12 0 3 8

10 -4 Solving Multistep Inequalities 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 Pre-Algebra