Answer: x = -2 and x = -6.
Explanation:
To solve the equation |3x + 12| = 6, we need to consider both the positive and negative cases for the absolute value expression.
Positive case: When the expression inside the absolute value is positive.
3x + 12 = 6
Now, let's solve for x:
Subtract 12 from both sides:
3x = 6 - 12
3x = -6
Divide by 3:
x = -6 / 3
x = -2
Negative case: When the expression inside the absolute value is negative.
-(3x + 12) = 6
Now, let's solve for x:
Distribute the negative sign:
-3x - 12 = 6
Add 12 to both sides:
-3x = 6 + 12
-3x = 18
Divide by -3:
x = 18 / -3
x = -6
So, the solutions to the equation |3x + 12| = 6 are x = -2 and x = -6.