1. 13.4 Solving Absolute Value Inequalities
Learning Targets:
I will be able to:
Solve an absolute value inequality
Compare multi-step, compound and absolute value inequalities

2. the distance between x and 0 is greater than 3.
Remember:
𝒙 = 3 means that the distance between x and 0 is 3.
𝒙 > 3 means that
the distance between x and 0 is greater than 3. 3
To write 𝒙 > 3 as an inequality
x < -3 OR x > 3.

3. To write 𝒙 < 3 as an inequality
𝒙 < 3 means that
the distance between x and 0 is less than 3. 3
To write 𝒙 < 3 as an inequality
-3< x < 3.

4. Solve: 𝒙−𝟒 <𝟔 Solution: -2 < x < 10
Remember:
The quantity inside the absolute value could be positive or negative.
Solve: 𝒙−𝟒 <𝟔
x – 4 < 6 and -(x – 4) < 6
x < 10
and
-x + 4 < 6
-x < 2
x > -2
Solution: < x < 10
This means that the solution is all real numbers less than 6 units from 4.

5. Solve: 𝟐𝒙+𝟏 >𝟓 2x + 1 > 5 OR -(2x + 1) > 5 2x + 1> 5 OR
Remember:
The quantity inside the absolute value could be positive or negative.
Solve: 𝟐𝒙+𝟏 >𝟓
2x + 1 > 5 OR -(2x + 1) > 5
2x + 1> 5
2x > 4
x > 2 OR
-2x - 1 > 5
-2x > 6
x <-3
Solution: x > 2 OR x < -3
This means that the solution is all real numbers more than 5 units from - 𝟏 𝟐 .

6. Solve and graph: 𝒙+𝟑 +𝟔≤𝟖

7. Solve and graph: 2 𝒙−𝟒 −𝟏≥ 7

8. Solve and graph: 3 𝒙+𝟕 +𝟏𝟎> 1

9. Solve and graph: 𝒙−𝟓 +𝟒< 1

10. Solve and graph: 1 2 𝒙 −𝟑< 2

11. Homework: Page 617 #1-21