LESSON How can you solve an inequality involving addition or subtraction? Addition and Subtraction Inequalities 13.2

Warm Up Write the inequality for each situation. 1. There are at least 28 days in a month. 2. The temperature is above 72°. 3. At most 9 passengers can ride in the van. days in a month ≥ 28 temperature > 72° passengers ≤ 9

When you add or subtract the same number on both sides of an inequality, the resulting statement will still be true. –2 < < 12 You can find solution sets of inequalities the same way you find solutions of equations, by isolating the variable.

Solve. Then graph the solution set on a number line. Additional Example 1A: Solving Inequalities by Adding n – 7 ≤ n ≤ 22 Add 7 to both sides. Draw a closed circle at 22 then shade the line to the left of –88-66

Solve. Then graph the solution set on a number line. Additional Example 1B: Solving Inequalities by Adding a – 10 ≥ – a ≥ 7 Add 10 to both sides. Draw a closed circle at 7. Then shade the line to the right. –4 –

Solve. Then graph the solution set on a number line. d – 12 ≤ – d ≤ –6 Add 12 to both sides. Draw a closed circle at –6 then shade the line to the left of –6. Check It Out: Example 1A –8 –6 –4 –

Solve. Then graph the solution set on a number line. b – 14 ≥ – b ≥ 6 Add 14 to both sides. Draw a closed circle at 6. Then shade the line to the right. –4 – Check It Out: Example 1B

You can check the solution to an inequality is true by choosing any number in the solution set and substituting it into the original inequality.

Solve. Check each answer. Additional Example 2A: Solving Inequalities by Subtracting d + 11 > 6 –11 d > –5 Check d + 11 > > 6 ? 11 > 6 ? Subtract 11 from both sides. 0 is greater than –5. Substitute 0 for d.

Solve. Check your answer. Additional Example 2B: Solving Inequalities by Subtracting b + 12 ≤ 19 –12 b 7 Check b + 12 ≤ Subtract 12 from both sides. 6 is less than 7. Substitute 6 for b. ≤ ? ? ≤ ≤

Solve. Check each answer. c + 15 > 9 –15 c > –6 Check c + 15 > > 9 ? 15 > 9 ? Subtract 15 from both sides. 0 is greater than –6. Substitute 0 for c. Check It Out: Example 2A

Solve. Check your answer. a + 15 ≤ 20 –15 a 5 Check a + 15 ≤ Subtract 15 from both sides. 4 is less than 5. Substitute 4 for a. ≤ ? ? ≤ ≤ Check It Out: Example 2B

When checking your solution, choose a number in the solution set that is easy to work with. Helpful Hint

Edgar’s August profit of $137 was at least $20 higher than his July profit. What was July’s profit? Additional Example 3: Money Application Let p represent the profit increase from July to August. 137 ≥ 20 + p ≥ p July’s profit was at most $117. Subtract 20 from both sides. August profit was at least $20 higher than July’s profit. $137 ≥ 20 + p p ≤ 117 Rewrite the inequality.

Rylan’s March profit of $172 was at least $12 less than his February profit. What was February’s profit? Check It Out: Example 3 Let p represent the profit decrease from February to march. 172 ≥ p ≥ p February’s profit was at most $184. Add 12 to both sides. March profit was at least $12 less than February’s profit. $172 ≥ p p ≤ 184 Rewrite the inequality.

ADDITIONAL EXAMPLE 1 Solve each inequality. Graph and check the solution. x + 3 ≥ –2A –6 < y –5B x ≥ –5 y > –1

ADDITIONAL EXAMPLE 2 Write a real-world problem that can be described by 14 < x + 7. Sample: A cook has 7 pounds of potatoes. He needs more than 14 pounds for dinner. What inequality describes the amount of potatoes the cook needs to buy?

13.2 LESSON QUIZ Solve each inequality. Graph and check the solution A 1.x + 20 ≥ –7 2.y − 30 ≤ 32

–16 < z – –2.5 > t Solve each inequality. Graph and check the solution.

Jeremy’s goal is to earn at least $80 toward a week at soccer camp. He has earned $32 so far. How much more does he need to earn? 5. Write and solve an inequality for each situation.

Do all values in the solution make sense for the situation? Explain. No. A negative value would make no sense, and 0 would mean that the suitcase is empty. 6.The maximum weight an airline allows for a suitcase is 50 pounds. Ella’s suitcase weighs 8 pounds empty. If Ella meets the requirements, what could be the weight of the contents of her suitcase? Write and solve an inequality for each situation. a. b.

How can you solve an inequality involving addition or subtraction? Sample answer: You can use the Addition and Subtraction Properties of Inequality: add or subtract the same amount from both sides to isolate the variable.