Question

In the following exercises, solve

$\left|4x-1\right|-3=0$

Short answer

The required solution is

$x=-\frac{1}{2}or1$

Step-by-step solution

Given information

$\left|4x-1\right|-3=0$

Calculation

$$\begin{gathered} \left|4x-1\right|-3=0 \\ \Rightarrow \left|4x-1\right|=3 \\ Theequivalentequationsare \\ \Rightarrow 4x-1=-3or4x-1=3 \\ \Rightarrow 4x=-3+1or4x=3+1 \\ \Rightarrow 4x=-2or4x=4 \\ \Rightarrow x=-\frac{1}{2}orx=1 \end{gathered}$$

The required solution is$x=\frac{-1}{2}or1$