1. 3-2 Solving Inequalities Using Addition and Subtraction
Hubarth
Algebra

2. Properties
Addition Property of Inequality
For every real number a, b, and c,
if 𝑎>𝑏, 𝑡ℎ𝑒𝑛 𝑎+𝑐>𝑏+𝑐 if 𝑎<𝑏, 𝑡ℎ𝑒𝑛 𝑎+𝑐<𝑏+𝑐
Examples 3>1, 𝑠𝑜 3+2>1+2 −5<4, 𝑠𝑜 −5+2<4+2
This property is also true for ≥ and ≤.
Subtraction Property of Inequality
For every real number a, b, and c,
if 𝑎>𝑏, 𝑡ℎ𝑒𝑛 𝑎−𝑐>𝑏−𝑐 if 𝑎<𝑏, 𝑡ℎ𝑒𝑛 𝑎−𝑐<𝑏−𝑐
Examples 3>1, 𝑠𝑜 3−2>1−2 −5<4, 𝑠𝑜 −5−2<4−2
This property is also true for ≥ and ≥.

3. Ex 1 Using the Addition Property of Inequality
Solve p – 4 < 1. Graph the solution.
p – < Add 4 to each side.
p < 5 Simplify.

4. Ex 2 Solving and Checking Solutions
Solve 8 d – 2. Graph and check your solution.
>
d – Add 2 to each side.
>
10 d, or d Simplify.
>
<
Check: 8 = d – 2 Check the computation.
– 2 Substitute 10 for d.
8 = 8
8 ≥ d – 2 Check the direction of the inequality.
8 ≥ 9 – Substitute 9 for d.
8 ≥ 7

5. Ex 3 Using the Subtraction Property of Inequality
Solve c + 4 > 7. Graph the solution.
c + 4 – 4 > 7 – 4 Subtract 4 from each side.
c > 3 Simplify.

6. Practice
Solve and graph each solution.
1. m – 6 > -4
m>2 2
2. n – 7 ≤ -2
𝑛≤5 5
3. t + 3 ≥ 8
𝑡≥5 5