Question

Solve each equation. Check your solution

$2\left|b+4\right|=48$

Short answer

The solutions of the equations is 20 or -28

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 x=y.
• Secondly assume the case two in which the equation be x=-y.
• 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- $x=y$

$\begin{array}{c}2b+8=48\\ 2b=48-8\\ b=\frac{40}{2}\end{array}$

Case2- $x=-y$

$\begin{array}{c}2b+8=-48\\ 2b=-48-8\\ b=\frac{-56}{2}\end{array}$

Step3- Check the solutions

Put the value of b=-28 in the equation $2\left|b+4\right|=48$

$\begin{array}{c}2|-28+4|=2|-24|\\ =2\times 24\\ =48\end{array}$

Put the value of b=20 in equation $2\left|b+4\right|=48$

$\begin{array}{c}2|20+4|=2\left|24\right|\\ =2\times 24\\ =48\end{array}$

The solution is 20 or -28. Hence, the solution set is (20,-28).