Solve for x: - 3|2x + 6| = -12
x = 1 and x = 5
x = -1 and x = -5
x = -9 and x = 3
No solution

Solution:

We will find the value of x which satisfies the equation - 3|2x + 6| = -12.

Step 1:

Divide both the sides by -3.

|2x + 6| = 4

As we can see that the equation has an absolute value, we will have two values x.

Step 2:

Put equations equal to 4 and -4 to get the values.

2x + 6 = 4 or 2x + 6 = - 4

Step 3:

By solving the equations, we get

2x = 4 - 6 or 2x = - 4 - 6

2x = -2 or 2x = -10

Step 4:

Divide both the sides by 2.

x = -1 or x = -5

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Solve for x: - 3|2x + 6| = -12
x = 1 and x = 5,  x = -1 and x = -5,  x = -9 and x = 3, No solution

Summary:

The solution for x are -5 or -1 for the equation - 3|2x + 6| = -12.