CPM Homework Help : GB8I Problem 9-82

Solve the inequalities below. Graph your solutions on a number line.

Hint (all):

Read Math Note box in Lesson 9.1.3 on solving inequalities and 9.2.2 on solving absolute value equations.

$| b - 4 | < 36$

Step 1(a):

Make sure the $|\text{__}|$ symbols are isolated. Then set $b − 4 = 36$ and $b − 4 = −36$

Step 2(a):

Solve for $b$ in both equations. These are your boundary points. Graph them on a number line.
Remember $<$ boundary point is not included and $≤$ boundary is included.

Step 3(a):

Test a point above, between, and below the boundary point in the original absolute value equation.
If it is true that portion of the line contains solutions to the inequality.
If it is false that portion of the line does not contain solutions to the inequality.

Answer (a):

$−32 < b < 40$

$| 3 + x | - 9 \geq 21$
Hint (b):
Follow steps from part (a):