-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