Since this is an absolute value equation, there are two solutions: one that produces the given value and one that produces the opposite of the given value.

-5x - 2 = 12

-5x = 14

**x = -2.8**

-5x - 2 = -12

-5x = -10

**x = 2**

** **

You can also answer this question graphically.

Graph: y = abs(-5x - 2)

Graph: y = 12

Find the two points of intersection. The x-values of these points are the two solutions to the equation.

We have to find the values of x that satisfy: |-5x-2|=12

|-5x-2|=12

=> -5x - 2 = 12 and -5x - 2 = -12

=> -5x = 14 and -5x = -10

=> x = -14/5 and x = 2

**The solution of the equation is x = -14/5 and x = 2**

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}.**