Question

Solve each equation. Check your solution

$\left|6c-1\right|=-2$

Short answer

The solutions of the equations is$\left(\varphi \right)$.

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  

Case1- $a=b$

$\begin{array}{c}6c-1=-2\\ 6c=-2+1\\ c=-\frac{1}{6}\end{array}$

Case2- $a=-b$

$\begin{array}{c}6c-1=-(-2)\\ 6c=2+1\\ c=\frac{3}{6}\end{array}$

Step3- Check the solutions

Put the value of $c=\frac{1}{2}$in the equation $\left|6c-1\right|=-2$

$\begin{array}{c}|6c-1|=|6\frac{1}{2}-1|\\ =|3-1|\\ =2\end{array}$

This is not true solution.

Put the value of $c=-\frac{1}{6}$in the equation $\left|6c-1\right|=-2$

$\begin{array}{c}|6c-1|=|6\times -\frac{1}{6}-1|\\ =|-1-1|\\ =|-2|\\ =2\end{array}$

The solution is not true. Hence, the solution set is $\left(\varphi \right)$.