Question

Solve the following equation: |x+5|=42

-42, 42

-5, 5

-37, 47

-47, 37

Answer 1

For absolute value equations, you must solve two equations by removing the | |
The First equation is simply
x + 5 = 42
The second equation makes the right hand side negative (Because whatever was inside the | | could be either positive or negative, and still give a postive answer)
x + 5 = -42
Solving for x will give you
37, -47.

For any future problems of the form
|x±a| = b
The two equations will be
x±a = b
x±a = -b

Answer 2

Just remember that absolute values | | are the distance between the number and 0. That will always be positive.
If we had |-2|=2.
What do you think it will be?