1. Solving Multi-Step Inequalities
Algebra 1 ~ Chapter 6-3
Solving Multi-Step Inequalities

2. Inequalities that contain more than one operation require more than one step to solve.
Use inverse operations to undo the operations in the inequality one at a time.
ALWAYS check your solution!

3. Example 1 - Solve the inequality and graph the solutions.
Check, b = 10
45 + 2b > 61
45 + 2(10) > 61
> 61
65 > 61
45 + 2b > 61
– –45
2b > 16
b > 8
Check, b = 6
45 + 2b > 61
45 + 2(6) > 61
> 61
57 > 61 2 4 6 8 10 12 14 16 18 20

4. Ex. 2 - Solve the inequality and graph the solutions.
– –8
Check, y = -8
8 – 3y ≥ 29
8 – 3(-8) ≥ 29
≥ 29
32 ≥ 29
–3y ≥ 21
by a negative #
y ≤ –7
–10 –8 –6 –4 –2 2 4 6 8 10 –7

5. Check, x = -7 -12 ≥ 3x + 6 -12 ≥ 3(-7) + 6 -12 ≥ -21 + 6 -12 ≥ -15
Ex. 3 - Solve the inequality and graph the solutions. Check your answer.
–12 ≥ 3x + 6
Check, x = -7
-12 ≥ 3x + 6
-12 ≥ 3(-7) + 6
-12 ≥
-12 ≥ -15
–12 ≥ 3x + 6
– – 6
–18 ≥ 3x
–6 ≥ x or x ≤ -6
–10 –8 –6 –4 –2 2 4 6 8 10

6. Ex. 4 - Solve the inequality and graph the solutions. Check your answer.
Check, x = -13
–5 –5
x + 5 < –6
> 3
x < –11
> 3
–20
–12 –8 –4
–16
–11
4 > 3

7. Example 5 - Solve the inequality and graph the solutions.
Check, x = 2
–4(2 – x) ≤ 8
-4(2 – 2) ≤ 8
-4(0) ≤ 8
0 ≤ 8
−4(2 – x) ≤ 8
–8 + 4x ≤ 8
x ≤ 4
–10 –8 –6 –4 –2 2 4 6 8 10

8. Example 6 - Solve the inequality and graph the solutions
Example 6 - Solve the inequality and graph the solutions. Check your answer.
3 + 2(x + 4) > 3
3 + 2(x + 4) > 3
Check, x = 0
3 + 2(x + 4) > 3
3 + 2(0 + 4) > 3
3 + 2(4) > 3
3 + 8 > 3
11 > 3
3 + 2x + 8 > 3
2x + 11 > 3
– 11 – 11
2x > –8
x > –4
–10 –8 –6 –4 –2 2 4 6 8 10

9. Lesson Review Solve each inequality and graph the solutions. x ≤ –4

10. Assignment Worksheet 6-3 Pages 335-336 #’s 16-28 (evens),