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Solving Inequalities Using Addition and Subtraction

p – 4 + 4 < 1 + 4 Add 4 to each side. p < 5 Simplify. Solving Inequalities Using Addition and Subtraction. ALGEBRA 1 LESSON 10-2. Solve p – 4 < 1. Graph the solutions. 10-2. 8 + 2 d – 2 + 2 Add 2 to each side. >. >. >. >. >. >. 10 d , or d 10 Simplify. <.

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Solving Inequalities Using Addition and Subtraction

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  1. p – 4 + 4 < 1 + 4Add 4 to each side. p < 5 Simplify. Solving Inequalities Using Addition and Subtraction ALGEBRA 1 LESSON 10-2 Solve p – 4 < 1. Graph the solutions. 10-2

  2. 8 + 2d – 2 + 2Add 2 to each side. > > > > > > 10 d, or d 10 Simplify. < Check: 8 = d – 2 Check the computation. 8 10 – 2 Substitute 10 for d. 8 = 8 8 d – 2 Check the direction of the inequality. 8 9 – 2 Substitute 9 for d. 8 7 Solving Inequalities Using Addition and Subtraction ALGEBRA 1 LESSON 10-2 Solve 8 d – 2. Graph and check your solution. 10-2

  3. c + 4 – 4 > 7 – 4Subtract 4 from each side. c > 3 Simplify. Solving Inequalities Using Addition and Subtraction ALGEBRA 1 LESSON 10-2 Solve c + 4 > 7. Graph the solutions. 10-2

  4. is more than points    points earned required points needed Relate: plus Define: Let = the number of points needed. p p Write: 120 + 90 + 350 > Solving Inequalities Using Addition and Subtraction ALGEBRA 1 LESSON 10-2 In order to receive a B in your literature class, you must earn more than 350 points of reading credits. Last week you earned 120 points. This week you earned 90 points. How many more points must you earn to receive a B? 10-2

  5. 120 + 90 + p > 350 210 + p > 350 Combine like terms. 210 + p– 210 > 350 – 210Subtract 210 from each side. p > 140 Simplify. Solving Inequalities Using Addition and Subtraction ALGEBRA 1 LESSON 10-2 (continued) You must earn 141 more points. 10-2

  6. > > w < –6 x > –2 p 2 > > 4 h, or h 4 < Solving Inequalities Using Addition and Subtraction ALGEBRA 1 LESSON 10-2 Solve each inequality. Graph the solutions. 1.p – 7 –5 2.w – 3 < –9 3.x + 6 > 4 4. 13 9 + h 10-2

  7. 3 > 3(–2) Multiply each side by 3. Do not reverse the inequality symbol. z 3 Check: = –2 Check the computation. 6 3 – = –2 Substitute –6 for z. –2 = –2 Simplify. ( ) z 3 z 3 > –2 Check the direction of the inequality. – > –2 Substitute –3 for z. 3 3 –1 > –2 Simplify. Solving Inequalities Using Multiplication and Division ALGEBRA 1 LESSON 10-2 z 3 Solve > –2. Graph and check the solutions. z > –6 Simplify each side. 10-2

  8. > < < 3 5 Multiply each side by the reciprocal of – , which is – , and reverse the inequality symbol. 5 3 ( ) ( ) 5 3 5 3 (3) – – –5 x, or x –5 Simplify. ( ) -3 5 x > Solving Inequalities Using Multiplication and Division ALGEBRA 1 LESSON 10-2 3 5 Solve 3 – x. Graph and check the solutions. 10-2

  9. < < < Solving Inequalities Using Multiplication and Division ALGEBRA 1 LESSON 10-2 (continued) Check:  3 = – xCheck the computation. 3 = – (–5) Substitute –5 for x. 3 = 3 3 – xCheck the direction of the inequality. 3 – (–10) Substitute –10 for x. 3 6 3 5 3 5 3 5 3 5 10-2

  10. –4c –4 24 –4 Divide each side by –4. Reverse the inequality symbol. > Solving Inequalities Using Multiplication and Division ALGEBRA 1 LESSON 10-2 Solve –4c < 24. Graph the solutions. c > –6 Simplify. 10-2

  11. is at most number of tanks cost per    total fuel tank budget Define: Let = the number of tanks of gas. Relate: times t t Write: 25 • 160 < < < < 25t 25 160 25 Divide each side by 25. 25t 160 t 6.4 Simplify. Solving Inequalities Using Multiplication and Division ALGEBRA 1 LESSON 10-2 Your family budgets $160 to spend on fuel for a trip. How many times can they fill the car’s gas tank if it cost $25 each time? Your family can fill the car’s tank at most 6 times. 10-2

  12. > > p > 3 y –6 > x < 5 –4 h, or h –4 > < Solving Inequalities Using Multiplication and Division ALGEBRA 1 LESSON 10-2 Solve each inequality. Graph the solution. 1. –3 2. – < –1 3. 6x < 30 4. 48 –12h y 2 p 3 10-2

  13. 5 + 4b– 5 < 21 – 5Subtract 5 from each side. 4b < 16 Simplify. 4b 4 16 4 < Divide each side by 4. b < 4 Simplify. Check:  5 + 4b = 21 Check the computation. 5 + 4(4) 21 Substitute 4 for b. 21 = 21 5 + 4b < 21 Check the direction of the inequality. 5 + 4(3) < 21 Substitute 3 for b. 17 < 21 Solving Multi-Step Inequalities ALGEBRA 1 LESSON 10-2 Solve 5 + 4b < 21. 10-2

  14. can be nomore than twice thewidth twice the    the length length of trim Relate: plus < Write: 2(20) + 2w 48 Solving Multi-Step Inequalities ALGEBRA 1 LESSON 10-2 The band is making a rectangular banner that is 20 feet long with trim around the edges. What are the possible widths the banner can be if there is no more than 48 feet of trim? 10-2

  15. 2(20) + 2w 48 40 + 2w 48 Simplify 2(20). 40 + 2w– 40 48 – 40Subtract 40 from each side. < < < < < < 2w 8 Simplify. Divide each side by 2. 2w 2 8 2 w 4 Simplify. Solving Multi-Step Inequalities ALGEBRA 1 LESSON 10-2 (continued) The banner’s width must be 4 feet or less. 10-2

  16. 3x + 24 – 4x < 2 Use the Distributive Property. –x + 24 < 2 Combine like terms. –x + 24 – 24 < 2 – 24Subtract 24 from each side. –x < –22 Simplify. –x –1 –22 –1 > Divide each side by –1. Reverse the inequality symbol. x > 22 Simplify. Solving Multi-Step Inequalities ALGEBRA 1 LESSON 10-2 Solve 3x + 4(6 – x) < 2. 10-2

  17. 8z – 6 – 3z < 3z + 12 – 3zSubtract 3z from each side. 5z – 6 < 12 Combine like terms. 5z – 6 + 6 < 12 + 6 Add 6 to each side. 5z < 18 Simplify. 5z 5 18 5 < Divide each side by 5. 3 5 z < 3 Simplify. Solving Multi-Step Inequalities ALGEBRA 1 LESSON 10-2 Solve 8z – 6 < 3z + 12. 10-2

  18. –15 + 5d 9d – 6 Use the Distributive Property. > –15 + 5d– 9d 9d – 6 – 9dSubtract 9d from each side. –15 – 4d –6 Combine like terms. –15 – 4d+ 15 –6 + 15Add 15 to each side. < < < < < < –4d 9 Simplify. Divide each side by –4. Reverse the inequality symbol. –4d –4 9 –4 > 1 4 d –2 Simplify. Solving Multi-Step Inequalities ALGEBRA 1 LESSON 10-2 Solve 5(–3 + d) 3(3d – 2). 10-2

  19. < a 3 > > 1 5 p > 7 1 3 c –3 < Solving Multi-Step Inequalities ALGEBRA 1 LESSON 10-2 Solve each inequality. 1. 8 + 5a 23 2. – p < p – 6 3. 3(x – 4) > 4x + 7 4. 3(3c + 2) 2(3c – 2) 1 3 1 2 x < –19 10-2

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