Question

Solve each equation. Check your solution

$\left|2z-3\right|=0$

Short answer

The solutions of the equations is$\frac{3}{2}$

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- $a=b$

$\begin{array}{c}2z-3=0\\ 2z=3+0\\ z=\frac{3}{2}\end{array}$

Case2- $a=-b$

$\begin{array}{c}2z-3=-0\\ 2z=3-0\\ z=\frac{3}{2}\end{array}$

Step3- Check the solutions

Put the value of $z=\frac{3}{2}$in the equation $\left|2z-3\right|=0$

$\begin{array}{c}|2z-3|=|2\frac{3}{2}-3|\\ =|3-3|\\ =0\end{array}$

The solution is $\frac{3}{2}$. Hence, the solution set is $\left(\frac{3}{2}\right)$.