Question

Solve each equation. Check your solution

$\left|y-2\right|=34$

Short answer

The solutions of the equations is 36 or -32

Step-by-step solution

Step 1. 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

Step 2. Solve the equations

Case1

$\begin{array}{c}y-2=34\\ y=34+2\\ =36\end{array}$

Case2

$\begin{array}{c}y-2=-34\\ y=-34+2\\ =-32\end{array}$

Step 3. Check the solutions

Put the value of $y=36$in equation $\left|y-2\right|=34$.

$\begin{array}{c}\left|y-2\right|=34\\ \left|36-2\right|=34\end{array}$

Put the value of $y=-32$in equation $\left|y-2\right|=34$.

$\begin{array}{c}\left|y-2\right|=34\\ \left|-32-2\right|=\left|-34\right|=34\end{array}$

The solution is $36$ or $-32$. Hence the solution set is $(-32,36)$.