What are the values of x in the equation |-5x-2|=12?

Applying the module property, we'll have to solve two
cases:

1) -5x-2=12

-5x = 12 +
2

-5x = 14

x =
-14/5

-5x - 2 > 0 => -5x > 2 =>
x < -2/5

Since -14/5 < -2/5, the value of x
is accepted as solution of equation.

2)
-5x-2=-12

-5x = -12+2

-5x =
-10

x = 2

-5x-2 `<=`
0

x `>=` -2/5

Since 2
> -2/5, the value of x is accepted as solution of
equation.

The requested solutions of the
equation are: {-14/5 ; 2}.