LESSON

How can you solve an inequality involving addition or subtraction?

Addition and Subtraction Inequalities13.2

Texas EssentialKnowledge and Skills

The student is expected to:

Expressions, equations, and relationships—6.10.A

Model and solve one-variable, one-step inequalities that represent problems, including geometric concepts.

Expressions, equations, and relationships—6.9.B

Represent solutions for one-variable, one-step equations and inequalities on number lines.

Expressions, equations, and relationships—6.9.C

Write corresponding real-world problems given one-variable, one-step equations or inequalities.

Texas EssentialKnowledge and Skills

Determine if the given value(s) make(s) one-variable, one-step equations or inequalities true.

Mathematical Processes

6.1.D

Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

The student is expected to:

Expressions, equations, and relationships—6.10.B

ADDITIONAL EXAMPLE 1Solve each inequality. Graph and check the solution.

x + 3 ≥ –2A

–6 < y –5B

x ≥ –5

y > –1

ADDITIONAL EXAMPLE 2Write 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.

6.10.A

1. x + 20 ≥ –7

2. y − 30 ≤ 32

–16 < z –143.

4. –2.5 > t + 3.5

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.

Use what you know about adding and subtracting integers to model subtraction inequalities with algebra tiles.

See the model below for x – 2 ≤ 4. Remember that x – 2 and x + (–2) are equivalent. Also recall the concept of zero pairs.

Write an explanation of the way to use algebra tiles to solve subtraction inequalities. Be prepared to demonstrate the method to other students.

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.