Question

select the correct answer.
what is the solution to $3|x + 3| = 12?$

a. $x = 1$

b. $x = 1$ or $x = -4$

c. $x = 1$ or $x = -7$

d. no solutions exist.

Explanation:

Step1: Divide both sides by 3

To isolate the absolute - value expression, we divide both sides of the equation \(3|x + 3|=12\) by 3.

$$ \frac{3|x + 3|}{3}=\frac{12}{3} $$

Simplifying, we get \(|x + 3| = 4\).

Step2: Solve the absolute - value equation

The absolute - value equation \(|a|=b\) (where \(b\geq0\)) is equivalent to \(a = b\) or \(a=-b\).
For \(|x + 3| = 4\), we have two cases:

Case 1: \(x + 3=4\)

Subtract 3 from both sides of the equation:

$$ x+3 - 3=4 - 3 $$

So, \(x = 1\).

Case 2: \(x + 3=-4\)

Subtract 3 from both sides of the equation:

$$ x+3 - 3=-4 - 3 $$

So, \(x=-7\).

Answer:

C. \(x = 1\) or \(x=-7\)