91Ó°ÊÓ

For any real numbers $a,b$, where $bâ‰\yen 0$, if $\left|a\right|=b$ then $a=b$ or $a=-b$.

Consider the equation $3|x+6|=36$.

Divide both sides of the equation by 3.

Use the concept of absolute value equation as follows:

$x+6=12$or $x+6=-12$.

Case 1. Simplify $x+6=12$.

Subtract 12 from both sides of the equation and simplify as follows:

Case 2. Simplify $x+6=-12$.

Add 12 on both sides of the equation and simplify as follows:

$\begin{array}{l}x+6=−12\\ x+6+12=−12+12\\ x+18=0\\ x=−18\end{array}$

Therefore, the solution is $x=6,-18$.

Case 1. Substitute $x=6$in the equation $3|x+6|=36$and simplify as follows:

Case 2. Substitute $x=-18$in the equation $3|x+6|=36$and simplify as follows:

Since the left-hand side of the equation is equal to the right-hand side of the equation in both the cases therefore, the solution is $x=6,-18$.