How to solve this absolute value equation?

Isolate the absolute value brackets, subtract 4 from both sides:

-|3x + 6| = -3

Divide both sides by -1:

|3x + 6| = 3

Expand the absolute value brackets:

3x + 6 = ± 3

Solve for each case:

3x + 6 = 3

3x = -3

x = -1

3x + 6 = -3

3x = -9

x = -3

x = -3, -1

Always check your solutions before confirming them, in this case both solutions fit.

Subtract 4 from both sides:

-|3x + 6| = -3

Multiply both sides by -1:

|3x + 6| = 3

Absolute values have two cases. If 3x + 6 is positive, the absolute value leaves it unchanged. If 3x + 6 is negative, the absolute value reverses its sign to make it positive.

Positive case:

3x + 6 = 3

Subtract 6 from both sides:

3x = -3

Divide both sides by 3

x = -1

Negative case:

-(3x + 6) = 3

Apply the minus sign:

-3x - 6 = 3

Add 6 to both sides:

-3x = 9

Divide both sides by -3:

x = -3

The solutions are x = 1 and x = -3.

rewrite it as

|3 x + 6| = 3

then by the properties of abs value you know

you have either of two possibilities:

3x + 6 = 3

3x = -3

x = -1

OR

3x + 6 = -3

3x = -9

x = -3

Check and you will see that these are both valid solutions