Question

In the following exercises, solve.

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

Short answer

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

Step-by-step solution

Step 1. Given information 

Absolute value equation:$\left|4x-1\right|-3=0$

Step 2. Calculation 

We have,

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

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

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

$4x-1=-3$ or $4x-1=3$

$4x-1+1=-3+1$ or $4x-1+1=3+1$

$4x=-2$ or $4x=4$

$\frac{4x}{4}=\frac{-2}{4}$ or $\frac{4x}{4}=\frac{4}{4}$

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