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

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.

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.

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: -2 < x < 10 This means that the solution is all real numbers less than 6 units from 4.

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 .

Solve and graph: 𝒙+𝟑 +𝟔≤𝟖

Solve and graph: 2 𝒙−𝟒 −𝟏≥ 7

Solve and graph: 3 𝒙+𝟕 +𝟏𝟎> 1

Solve and graph: 𝒙−𝟓 +𝟒< 1

Solve and graph: 1 2 𝒙 −𝟑< 2

Homework: Page 617 #1-21