-4 |2x +1| = -12

To find the solution to the equation, we need to isolate the absolute value expression on one side of the equation.

First, divide both sides of the equation by -4:

|2x + 1| = -12/-4

Simplifying, we get:

|2x + 1| = 3

Since the absolute value of a number cannot be negative, we know that the expression inside the absolute value must either be positive or negative.

Case 1: 2x + 1 is positive

2x + 1 = 3

Subtracting 1 from both sides, we have:

2x = 2

Dividing both sides by 2, we get:

x = 1

Case 2: 2x + 1 is negative

-2x - 1 = 3

Adding 1 to both sides, we have:

-2x = 4

Dividing both sides by -2, we get:

x = -2

Therefore, the two solutions to the equation are x = 1 and x = -2