Solve each inequality. Graph the solution set on a number line. 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

ANSWERS 1. x > 18 2. g ≤ –23 3. t ≤ 19 4. d > 28; 5. f ≤ –5; 6. $26.50 Course 2, Lesson 6-7

two quantities are equal? Expressions and Equations WHAT does it mean to say two quantities are equal? Course 2, Lesson 6-7

Solve word problems leading to inequalities of the form px + q > r Expressions and Equations 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.

Mathematical Practices Expressions and Equations 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.

To solve inequalities when multiplying Expressions and Equations 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

Multiplication Property of Inequality Division Property of Inequality Expressions and Equations Multiplication Property of Inequality Division Property of Inequality Course 2, Lesson 6-7

Multiplication and Division Properties of Inequality, Positive Number Expressions and Equations Multiplication and Division Properties of Inequality, Positive Number 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 Course 2, Lesson 6-7

The solution is x ≤ 5. You can check this solution by Step-by-Step Example 1. Solve 8x ≤ 40. 1 8x ≤ 40 Write the inequality. 2 Divide each side by 8. 3 x ≤ 5 Simplify. 4 The solution is x ≤ 5. You can check this solution by substituting 5 or a number less than 5 into the inequality. Need Another Example?

Need Another Example? Solve 5x > 30. x > 6 Answer

The solution is d > 14. You can check this solution by Step-by-Step Example 2. Solve > 7. > 7 1 Write the inequality. 2 > 2(7) 2 Multiply each side by 2. 3 d > 14 Simplify. 4 The solution is d > 14. You can check this solution by substituting a number greater than 14 into the inequality. Need Another Example?

Need Another Example? Solve 3 ≥ . 12 ≥ h or h ≤ 12 Answer

Multiplication and Division Properties of Inequality, Negative Number Expressions and Equations Multiplication and Division Properties of Inequality, Negative Number 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. Course 2, Lesson 6-7

Solve −2g < 10. Graph the solution set on a number line. Step-by-Step Example 3. Solve −2g < 10. Graph the solution set on a number line. 1 – 2g < 10 Write the inequality. 2 Divide each side by –2 and reverse the symbol. 3 g > –5 Simplify. 4 Need Another Example?

Solve –4x ≤ 4. Graph the solution set on a number line. Need Another Example? Solve –4x ≤ 4. Graph the solution set on a number line. x ≥ –1 Answer

Solve ≤ 4. Graph the solution set on a number line. Step-by-Step Example 4. Solve ≤ 4. Graph the solution set on a number line. ≤ 4 1 Write the inequality. 2 Multiply each side by –3 and reverse the symbol. 3 x ≥ –12 Simplify. 4 Need Another Example?

Solve > – 5. Graph the solution set on a number line. Need Another Example? Solve > – 5. Graph the solution set on a number line. x < 20 Answer

Ling earns $8 per hour working at the zoo. Write and solve an 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. 1 Word Amount earned times number is at amount earned per hour of hours least each week. Variable Let x represent the number of hours. Inequality 8 x ≥ 120 8x ≥ 120 2 Write the inequality. 3 Divide each side by 8. 4 x ≥ 15 Simplify. So, Ling must work at least 15 hours. 5 Need Another Example?

A plate weighs pound. A shelf can hold at most 20 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. Answer

How did what you learned today help you answer the Expressions and Equations 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

How did what you learned today help you answer the Expressions and Equations How did what you learned today help you answer the WHAT does it mean to say two quantities are equal? 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 Course 2 Lesson 6-7

Expressions and Equations Ratios and Proportional Relationships How did the previous lesson on solving inequalities by adding or subtracting help you with today’s lesson? Course 2 Lesson 6-7