Question

Solve the equation and check the solution.

$3|x+6|=36$

Short answer

The solution is $x=6,-18$.

Step-by-step solution

Step 1- Apply the concept of absolute value.

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

Step 2- Step description.

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

Divide both sides of the equation by 3.

$\begin{array}{l}3|x+6|=36\\ |x+6|=\frac{36}{3}\\ |x+6|=12\end{array}$

Use the concept of absolute value equation as follows:

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

Step 3- Step description.

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

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

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

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 $x=6,-18$.

Step 4- Verify the solution.

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

$\begin{array}{l}3|x+6|=36\\ 3|6+6|=36\\ 3\left|12\right|=36\\ 3\left(12\right)=36\\ 36=36\end{array}$

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

$\begin{array}{l}3|x+6|=36\\ 3|-18+6|=36\\ 3|-12|=36\\ 3\left(12\right)=36\\ 36=36\end{array}$

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 $x=6,-18$.