Question

Solve each equation. Check your solution

$\left|c-2\right|=2c-10$

Short answer

The solutions of the equations is$\mathbf{8}$.

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 on the left and right sides

Step 2. Solve the equations

Case1

$\begin{array}{c}a=b\\ c-2=2c-10\\ 2c-c=10-2=8\\ c=8\end{array}$

Case2

$\begin{array}{c}a=-b\\ c-2=-2c+10\\ 2c+c=10+2=12\\ 3c=12\\ c=4\end{array}$

Step 3. Check the solutions

Put the value of $c=8$ in equation$\left|c-2\right|=2c-10$

$\begin{array}{c}\left|c-2\right|=2c-10\\ \left|8-2\right|=2\times 8-10=6\end{array}$

Put the value of $c=4$ in equation $\left|c-2\right|=2c-10$

$\begin{array}{c}\left|c-2\right|=2c-10\\ \left|4-2\right|=2\left(4\right)-10\\ 2=-2\end{array}$

Hence the solution is never true.

The solution is 8. Hence the solution set is $\left(8\right)$.