Solve each of the following in equations and represent the solution set on

Solution:

Given:

$|4 x-5| \leq \frac{1}{3}, x \in R$

$4 x-5 \leq \frac{1}{3}$ or $4 x-5 \geq-\frac{1}{3}$

$4 x-5 \leq \frac{1}{3}$

Adding 5 to both the sides in the above equation

$4 x-5+5 \leq \frac{1}{3}+5$

$4 x \leq \frac{1+15}{3}$

$4 x \leq \frac{16}{3}$

Now, dividing both the sides by 4 in the above equation

$\frac{4 x}{4} \leq \frac{16}{3 \cdot(4)}$

$x \leq \frac{4}{3}$

Now

$4 x-5 \geq-\frac{1}{3}$

Adding 5 to both the sides in the above equation

$4 x-5+5 \geq-\frac{1}{3}+5$

$4 x \geq \frac{-1+15}{3}$

$4 x \geq \frac{14}{3}$

Now, dividing both the sides by 4 in the above equation

$\frac{4 x}{4} \geq \frac{14}{3 .(4)}$

$x \geq \frac{7}{6}$

Therefore

$x \in\left[\frac{7}{6}, \frac{4}{3}\right]$