Question

Solve each equation. Check your solution

$\left|b+15\right|=3$

Short answer

The solutions of the equations is -18 or -12

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

Case 1

$\begin{array}{c}x=y\\ b+15=3\\ b=-15+3\\ =-12\end{array}$

Case2

$\begin{array}{c}x=-y\\ b+15=-3\\ b=-15-3\\ =-18\end{array}$

Step3- Check the solutions

Put the value of b=-12 in equation

$\left|b+15\right|=3$

$\begin{array}{c}|-12+15|=\left|3\right|\\ =3\end{array}$

Put the value of b=-18 in equation $\left|b+15\right|=3$

$\begin{array}{c}|-18+15|=|-3|\\ =3\end{array}$

The solution is -18or-12.Hence the solution set is (-18,-12).