Question

Solve each equation. Check your solution

$8\left|w-7\right|=72$

Short answer

The solutions of the equations is 16 or -2

Step-by-step solution

Step1- Order for solving the equation

To evaluate any equation involving more than one operation, follow the below order operation

• First assume the case one in which the equation be a=b.
• Secondly assume the case two in which the equation be a=-b.
• Solve the equations of both the cases to find the value of algebraic expression
• After finding the two values of algebraic expression, put the value in the original equation and check the solution

Step2- Solve the equations  

Case1: $a=b$

$\begin{array}{c}8w-56=72\\ 8w=72+56\\ w=\frac{128}{8}\\ =16\end{array}$

Case2:$a=-b$

$\begin{array}{c}8w-56=-72\\ 8w=-72+56\\ w=-\frac{16}{8}\\ =-2\end{array}$

Step3- Check the solutions

Put the value of w=2 in the equation $8\left|w-7\right|=72$

$\begin{array}{c}8|w-7|=8|-2-7|\\ =8|-9|\\ =8\times 9\\ =72\end{array}$

Put the value of w=16 in equation $8\left|w-7\right|=72$

$\begin{array}{c}8|16-7|=8\left|9\right|\\ =8\times 9\\ =72\end{array}$

The solution is 16 or -2.