Lesson Menu Main Idea and New Vocabulary Example 1:Write Inequalities Example 2:Write Inequalities Example 3:Write Inequalities Example 4:Write Inequalities Example 5:Determine the Truth of an Inequality Example 6:Determine the Truth of an Inequality Example 7:Graph an Inequality Example 8:Graph an Inequality

Main Idea/Vocabulary Write and graph inequalities. inequality

Example 1 Write Inequalities Write an inequality for the sentence. Johann needs less than 2 hours to paint his room. Let r = the number of hours. Answer: r < 2

Example 1 CYP A.c < 5 B.c > 5 C.c ≤ 5 D.c ≥ 5 Write an inequality for the sentence. More than 5 cups of popcorn are needed to make popcorn balls.

Example 2 Write an inequality for the sentence. Lena walked more than 20 miles for charity. Write Inequalities Let w = the number of miles. Answer: w > 20

Example 2 CYP A.d < 3 B.d > 3 C.d ≤ 3 D.d ≥ 3 Write an inequality for the sentence. Josh has less than 3 days to return his library books.

Example 3 Write Inequalities Write an inequality for the sentence. At least $30 must be spent to get a discount on the groceries. Let g = the amount spent on groceries. Answer: g ≥ 30

Example 3 CYP A.f < 7 B.f > 7 C.f ≤ 7 D.f ≥ 7 Write an inequality for the sentence. An aquarium can hold no more than 7 fish.

Example 4 Write an inequality for the sentence. There can be at most 5 people in the car. Write Inequalities Let p = the number of people. Answer: p ≤ 5

Example 4 CYP A.x > 6 B.x < 6 C.x ≥ 6 D.x ≤ 6 Write an inequality for the sentence. A plant needs at least 6 hours of sunlight.

Example 5 Determine the Truth of an Inequality State whether the inequality x – 4 < 6 is true or false for x = 0. x – 4 <6Write the inequality. – 4 <6Simplify. 0 – 4 <6Replace x with 0. ? Answer:Since –4 < 6 is true, the inequality is true for x = 0.

Example 5 CYP A.true B.false State whether the inequality 10  y – 3 is true or false for y = 8.

Example 6 Determine the Truth of an Inequality State whether the inequality 3x ≥ 4 is true or false for x = 1. 3x ≥ 4Write the inequality. 3(1) ≥ 4Replace x with 1. ? Answer:Since 3 is not greater than or equal to 4, 3 ≥ 4 is false. So, the inequality is false for x = 1. 3 ≥ 4Simplify.

Example 6 CYP A.true B.false State whether the inequality 6x  5 is true or false for x = –1.

Example 7 Graph an Inequality Graph the inequality n > –1 on a number line. Answer: Place an open dot at –1. Then draw a line and an arrow to the right.

Example 7 CYP Graph the inequality k < –3 on a number line. A. B. C. D.

Example 8 Graph an Inequality Graph the inequality n ≤ –1 on a number line. Answer: Place a closed dot at –1. Then draw a line and an arrow to the left.

Example 8 CYP Graph the inequality x > 4 on a number line. A. B. C. D.