(7) Lesson 6.7
- 1. Solve each inequality. 1. x – 15 > 3 2. g + 3 ≤ –20 3. 11 ≥ t – 8 Solve each inequality. Graph the solution set on a number line. 4. 34 < 6 + d 5. 5 – f ≥ 10 6. Jonas has $75 to spend on new clothes. The pair of jeans he wants costs $48.50. What is the most Jonas can spend on shirts? Course 2, Lesson 6-7
- 2. ANSWERS 1. x > 18 2. g ≤ –23 3. t ≤ 19 4. d > 28; 5. f ≤ –5; 6. $26.50 Course 2, Lesson 6-7
- 3. WHAT does it mean to say two quantities are equal? Expressions and Equations Course 2, Lesson 6-7
- 4. • 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. • 7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. Course 2, Lesson 6-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Expressions and Equations
- 5. Mathematical Practices 1 Make sense of problems and persevere in solving them. 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. 7 Look for and make use of structure. Course 2, Lesson 6-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Expressions and Equations
- 6. • To solve inequalities when multiplying or dividing by a positive number • To solve inequalities when multiplying or dividing by a negative number Course 2, Lesson 6-7 Expressions and Equations
- 7. Course 2, Lesson 6-7 Expressions and Equations • Multiplication Property of Inequality • Division Property of Inequality
- 8. Course 2, Lesson 6-7 Expressions and Equations Words The and the state that an inequality remains true when you multiply or divide each side of an inequality by a positive number. Symbols For all numbers a, b, and c, where c > 0, 1. if a > b, then ac > bc and 2. if a < b, then ac < bc and These properties are also true for a ≥ b and a ≤ b. Multiplication Property of Inequality Division Property of Inequality . a b c c . a b c c
- 9. 1 Need Another Example? 2 3 4 Step-by-Step Example 1. Solve 8x ≤ 40. Write the inequality. The solution is x ≤ 5. You can check this solution by substituting 5 or a number less than 5 into the inequality. Simplify. 8x ≤ 40 Divide each side by 8. x ≤ 5
- 10. Answer Need Another Example? Solve 5x > 30. x > 6
- 11. Need Another Example? Step-by-Step Example 2. Solve > 7. 1 2 3 4 Write the inequality. The solution is d > 14. You can check this solution by substituting a number greater than 14 into the inequality. Simplify. > 7 Multiply each side by 2. d > 14 2 > 2(7)
- 12. Answer Need Another Example? Solve 3 ≥ . 12 ≥ h or h ≤ 12
- 13. Course 2, Lesson 6-7 Expressions and Equations Words When you multiply or divide each side of an inequality by a negative number, the inequality symbol must be reversed for the inequality to remain true. Symbols For all numbers a, b, and c, where c < 0, 1. if a > b, then ac < bc and 2. if a < b, then ac > bc and Examples 7 > 1 –4 < 16 –2(7) < –2(1) Reverse the symbols > –14 < –2 1 > –4 These properties are also true for a ≥ b and a ≤ b. . a b c c . a b c c 4 4 16 4
- 14. 1 Need Another Example? 2 3 4 Step-by-Step Example 3. Solve −2g < 10. Graph the solution set on a number line. Write the inequality. Simplify. – 2g < 10 Divide each side by –2 and reverse the symbol. g > –5
- 15. Answer Need Another Example? Solve –4x ≤ 4. Graph the solution set on a number line. x ≥ –1
- 16. 1 Need Another Example? 2 3 4 Step-by-Step Example 4. Solve ≤ 4. Graph the solution set on a number line. Write the inequality. Simplify. ≤ 4 Multiply each side by –3 and reverse the symbol. x ≥ –12
- 17. Answer Need Another Example? Solve > – 5. Graph the solution set on a number line. x < 20
- 18. 1 Need Another Example? 2 3 4 5 Step-by-Step Example 5. Ling earns $8 per hour working at the zoo. Write and solve an inequality that can be used to find how many hours she must work in a week to earn at least $120. Interpret the solution. Write the inequality. Simplify. 8x ≥ 120 Divide each side by 8. x ≥ 15 Word Variable Inequality Amount earned times number is at amount earned per hour of hours least each week. Let x represent the number of hours. 8 x ≥ 120 So, Ling must work at least 15 hours.
- 19. Answer Need Another Example? A plate weighs pound. A shelf can hold at most 20 pounds. Write and solve an inequality to find how many plates the shelf can hold. Interpret the solution. x ≤ 20; x ≤ 80; The shelf can hold at most 80 plates.
- 20. How did what you learned today help you answer the WHAT does it mean to say two quantities are equal? Course 2 Lesson 6-7 Expressions and Equations
- 21. How did what you learned today help you answer the WHAT does it mean to say two quantities are equal? Course 2 Lesson 6-7 Expressions and Equations Sample answers: • To keep the same inequality sign when multiplying or dividing each side of an inequality by a positive number • To reverse the inequality sign when multiplying or dividing each side of an inequality by a negative number
- 22. How did the previous lesson on solving inequalities by adding or subtracting help you with today’s lesson? Ratios and Proportional RelationshipsExpressions and Equations Course 2 Lesson 6-7