Question

Solve each equation. Check your solution

$\left|x-25\right|=17$

Short answer

The solutions of the equations is42 or 8

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

$\begin{array}{c}x-25=17\\ x=25+17\\ x=42\end{array}$

Case 2 : a=-b

$\begin{array}{c}x-25=-17\\ x=25-17\\ x=8\end{array}$

Step3- Check the solutions

Put the value of x=8 in the equation $\left|x-25\right|=17$.

$\begin{array}{c}|x-25|=|8-25|\\ =|-17|\\ =17\end{array}$

Put the value of x=42 in equation $\left|x-25\right|=17$.

$\begin{array}{c}|x-25|=|42-25|\\ =\left|17\right|\\ =17\end{array}$

The solution is 42 or 8. Hence, the solution set is (42,8).