Question

Solve each equation. Check your solution

$\left|y+9\right|=21$

Short answer

The solutions of the equations are-30 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 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  

Case 1: a=b

$\begin{array}{c}y+9=21\\ y=21-9\\ =12\end{array}$

Case 2: a=-b

localid="1646755493379" $\begin{array}{c}y+9=-21\\ y=-21-9\\ =-30\end{array}$

Step3- Check the solutions

Put the value of y=12 in the equation $\left|y+9\right|=21$.

$\begin{array}{c}|y+9|=|12+9|\\ =21\end{array}$

Put the value of y=-30 in equation $\left|y+9\right|=21$

$\begin{array}{c}|y+9|=|-30+9|\\ =|-21|=21\end{array}$

The solution is -31 or 12.