Given:
[tex]|\frac{n}{3}|=2[/tex]
Let's solve the absolute value equation for n.
Take the following steps:
Step 1:
Remove the absolute value symbol, then add ± to the right hand side
[tex]\frac{n}{3}=\pm2[/tex]
Step 2:
Here, we have two conditions. Solve the equation for both values
[tex]\begin{gathered} \text{Condition 1:} \\ \frac{n}{3}=2 \\ \text{Multiply 3 to both sides:} \\ \frac{n}{3}\times3=2\times3 \\ \\ n=6 \end{gathered}[/tex][tex]\begin{gathered} \text{Condition 2:} \\ \frac{n}{3}=-2 \\ Multiply\text{ both sides by 3} \\ \frac{n}{3}\times3=-2\times3 \\ \\ n=-6 \end{gathered}[/tex]
The solution of the absolute value equation includes both the negative and positive values.
Thus, we have:
n = 6, -6
ANSWER:
n = 6 and -6
