Question

Solve for x: |2x + 12| = 18Group of answer choicesx = 3, x = −3x = 3, x = −15x = 15, x = −15x = −3, x = 15

Answer 1

The problem is given to be:

$|2x+12|=18$

Step 1: Apply the Absolute Rule stated below:

$\begin{gathered} If \\ |u|=a \\ \text{then} \\ u\: =\: a\: \quad \mathrm{or}\quad \: u\: =\: -a \end{gathered}$

Therefore, we have:

$\begin{gathered} 2x+12=18 \\ or \\ 2x+12=-18 \end{gathered}$

Step 2: Solve the first case:

$\begin{gathered} 2x+12=18 \\ Subracti\text{ng 12 from both sides:} \\ 2x=18-12 \\ 2x=6 \\ \text{Dividing both sides by 2:} \\ x=\frac{6}{2} \\ x=3 \end{gathered}$

Step 3: Solve the second case:

$\begin{gathered} 2x+12=-18 \\ \text{Subracting 12 from both sides:} \\ 2x=-18-12 \\ 2x=-30 \\ Divid\text{ing both sides by 2:} \\ x=\frac{-30}{2} \\ x=-15 \end{gathered}$

ANSWER:

The values of x are:

$x=3,x=-15$