2. Key Concept: Addition and Subtraction Properties of Inequality
Main Idea
Key Concept: Addition and Subtraction Properties of Inequality
Example 1: Solve Inequalities Using Subtraction and Addition
Example 2: Solve Inequalities Using Subtraction and Addition
Example 3: Graph Solutions of Inequalities
Example 4: Write an Inequality
Lesson Menu

3. Solve inequalities by using the Addition and Subtraction Properties of Inequality.
Main Idea/Vocabulary

4. Key Concept

5. Solve Inequalities Using Subtraction and Addition
Solve x + 5 > 12.
x + 5 > 12 Write the inequality.
x + 5 – 5 > 12 – 5 Subtract 5 from each side.
x > 7 Simplify.
Answer: The solution is x > 7.
Example 1

6. Solve x – 5 < 10. A. x < 5 B. x > 5 C. x < 15 D. x > 15
Example 1 CYP

7. Solve Inequalities Using Subtraction and Addition
Solve –8 ≥ y + 3.
–8 ≥ y + 3 Write the inequality.
–8 – 3 ≥ y + 3 – 3 Subtract 3 from each side.
–11 ≥ y Simplify.
Answer: The solution is –11 ≥ y or y ≤ –11.
Example 2

8. Solve 4 ≥ h + 1.
A. 5 ≥ h
B. 5 ≤ h
C. 3 ≥ h
D. 3 ≤ h
Example 2 CYP

9. Graph Solutions of Inequalities
Solve Graph the solution set on a number line.
Write the inequality.
Subtract from each side.
Rename 2 as a fraction with a denominator of 4.
Simplify.
Example 3

10. Graph Solutions of Inequalities
The solution is
Graph the solution.
Example 3

11. Graph Solutions of Inequalities
Answer: The solution is
Example 3

12. Solve d + < 6. Graph the solution set on a number line.C. D.
Example 3 CYP

13. We need to find the greatest amount of money Jerome can spend on CDs.
Write an Inequality
SHOPPING Jerome took $20 to the store to buy a book and some CDs. If he buys a book that costs $4.50, what is the most he could spend on CDs?
We need to find the greatest amount of money Jerome can spend on CDs.
Let y represent the amount Jerome can spend on CDs. Write an inequality to represent the problem. .
Example 4

14. 4.5 + y  20 Write the inequality. (4.50 = 4.5)
Write an Inequality
4.5 + y  20 Write the inequality. (4.50 = 4.5)
4.5 – y  20 – 4.5 Subtract 4.5 from each side.
y  15.5 Simplify.
Check by choosing an amount less than or equal to $15.50, such as $10. Then Jerome would spend $ $10 or $14.50 in all. Since $14.50 < $20, the answer is reasonable.
Answer: So, the most Jerome can spend on CDs is $15.50.
Example 4

15. BOWLING Monique took $15 to the bowling alley. Shoe rental costs $3.75. What is the most she could spend on games and snacks?
A. x < $12.25
B. x ≤ $11.25
C. x < $11.25
D. x > $11.25
Example 4 CYP