1. Solving Inequalities Using Addition and Subtraction
Unit 3 Lesson 2

2. SOLVING INEQUALITIES USING ADDITION AND SUBTRACTION
ADDITION PROPERTY OF INEQUALITIES “If any number is added to each side of a true inequality, the resulting inequality is also true.” For all numbers 𝒂, 𝒃, and 𝒄, the following are true:
1. 
If 𝒂>𝒃, then 𝒂+𝒄>𝒃+𝒄.
2. 
If 𝒂<𝒃, then 𝒂+𝒄<𝒃+𝒄.
𝟏𝟏>𝟖
𝟏𝟏+𝟐>𝟖+𝟐
𝟏𝟑>𝟏𝟎
𝟏𝟓<𝟐𝟏
𝟏𝟓+𝟓<𝟐𝟏+𝟓
𝟐𝟎<𝟐𝟔
3. 
If 𝒂≥𝒃, then 𝒂+𝒄≥𝒃+𝒄.
4. 
If 𝒂≤𝒃, then 𝒂+𝒄≤𝒃+𝒄.
𝟗≥𝟖
𝟗+𝟒≥𝟖+𝟒
𝟏𝟑≥𝟏𝟐
𝟏𝟑≤𝟏𝟒
𝟏𝟑+𝟑≤𝟏𝟒+𝟑
𝟏𝟔≤𝟏𝟕

3. SOLVING INEQUALITIES USING ADDITION AND SUBTRACTION
Sample Problem 1: Solve each inequality. A.
𝒙−𝟔≥𝟒 B.
𝒛−𝟒𝟓<𝟏𝟑

4. SOLVING INEQUALITIES USING ADDITION AND SUBTRACTION
Sample Problem 1: Solve each inequality. A.
𝒙−𝟔≥𝟒
𝒙−𝟔+𝟔≥𝟒+𝟔
𝒙≥𝟏𝟎 B.
𝒛−𝟒𝟓<𝟏𝟑
𝒛−𝟒𝟓+𝟒𝟓<𝟏𝟑+𝟒𝟓
𝒛<𝟓𝟖

5. SOLVING INEQUALITIES USING ADDITION AND SUBTRACTION
SUBTRACTION PROPERTY OF INEQUALITIES “If any number is subtracted to each side of a true inequality, the resulting inequality is also true.” For all numbers 𝒂, 𝒃, and 𝒄, the following are true:
1. 
If 𝒂>𝒃, then 𝒂−𝒄>𝒃−𝒄.
2. 
If 𝒂<𝒃, then 𝒂−𝒄<𝒃−𝒄.
𝟏𝟐>𝟕
𝟏𝟐+𝟓>𝟕+𝟓
𝟐𝟎>𝟏𝟐
𝟏𝟔<𝟐𝟎
𝟏𝟔+𝟑<𝟐𝟎+𝟑
𝟏𝟗<𝟐𝟑
3. 
If 𝒂≥𝒃, then 𝒂−𝒄≥𝒃−𝒄.
4. 
If 𝒂≤𝒃, then 𝒂−𝒄≤𝒃−𝒄.
𝟖≥𝟕
𝟖+𝟐≥𝟕+𝟐
𝟏𝟎≥𝟗
𝟏𝟐≤𝟏𝟓
𝟏𝟐+𝟒≤𝟏𝟓+𝟒
𝟏𝟔≤𝟏𝟗

6. SOLVING INEQUALITIES USING ADDITION AND SUBTRACTION
Sample Problem 2: Solve each inequality. A.
𝟐𝟎+𝒙≥𝟏𝟓 B.
𝒚+𝟓<𝟐𝟐

7. SOLVING INEQUALITIES USING ADDITION AND SUBTRACTION
Sample Problem 2: Solve each inequality. A.
𝟐𝟎+𝒙≥𝟏𝟓
𝟐𝟎−𝟐𝟎+𝒙≥𝟏𝟓−𝟐𝟎
𝒙≥−𝟓 B.
𝒚+𝟓<𝟐𝟐
𝒚+𝟓−𝟓<𝟐𝟐−𝟓
𝒚<𝟏𝟕