1. Solving Inequalities with variables on both sides of the Sign
Chapter 6.3

2. Solving Inequalities with variables on both sides of the Sign
Lesson Objective: NCSCOS Use linear functions to model and solve problems
Students will know how to solve equations with variables on both sides.
Students will know how to use the distributive property to solve problems.
Students will know how to combine like terms to solve problems

3. Solving Inequalities with variables on both sides of the Sign5x 2x
- 8 x
< 20 3x + 12
Example 1:
First we must get all the variables on one side of the equation.
Subtract 3x from both sides
Second we have to get all the numbers on the other side
Add 8 to both sides
Divide both sides by 2
-3x x

4. Solving Inequalities with variables on both sides of the Sign
6 – x > 5x + 30
5y – 4y ≥ 3y + 2
4m – 8 ≤ 10 – 2m
8 + 4k < k
(2/5)x – 8 ≤ 9 – (3/5)x
Practice

5. Solving Inequalities with variables on both sides of the Sign
Example 2:
Distribute on both sides
Add 10x to both sides
Add 4 to both sides
Divide by 18
4(2x – 1) ≥ -10(x – 5)
18x – 4 ≥ 50
8x – 4 ≥ -10x + 50
18x ≥ 54
x ≥ 3
+10x x

6. Solving Inequalities with variables on both sides of the Sign
-3(x + 5) < 3(x – 1)
5(x + 2) ≤ 2(3 – x)
4(m + 3) > 36
4(y – 2) < 2(5 – y)
3(x – 8) ≥ 3x
More Practice

7. Solving Inequalities with variables on both sides of the Sign
Example 3:
Distribute on both sides
Combine like terms on either side of the equals sign
Subtract 3x from both sides
Subtract 24 from both sides
Divide by 2
5(x + 3) + 9 > 3(x – 4) + 6
5x > 3x –
5x + 24 > 3x - 6
2x + 24 > -6 __
2x > -30
x > -15 __
-3x x

8. Solving Inequalities with variables on both sides of the Sign
3(x – 8) – 5 ≤ 9(x + 2) + 1
2(x + 2) + x ≥ 5 + 4(x – 2)
5x – (3x – 3) > 2x + 3(x + 4)
Last Practice!

9. Solving Inequalities with variables on both sides of the Sign
Quiz 6.3
2x + 3 ≤ 3x – 5
7x – 3 > 3 – 2x
2(x + 3) ≥ 3(x – 4)
5(2x – 4) < -6(2 – x)
3(x + 2) – 2x > 4(x -3) + 6