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

Solution:

Given:

$|5-2 x| \leq 3, x \in R .$

$5-2 x \geq-3$ or $5-2 x \leq 3$

$5-2 x \geq-3$

Subtracting 5 from both the sides in the above equation

$5-2 x-5 \geq-3-5$

$-2 x \geq-8$

Now, multiplying by -1 on both the sides in the above equation

$-2 x(-1) \geq-8(-1)$

$2 x \leq 8$

Now dividing by 2 on both the sides in the above equation

$\frac{2 x}{2} \leq \frac{8}{2}$

$x \leq 4$

$5-2 x \leq 3$

Subtracting 5 from both the sides in the above equation

$5-2 x-5 \leq 3-5$

$-2 x \leq-2$

Now dividing by 2 on both the sides in the above equation

$\frac{2 x}{2} \geq \frac{2}{2}$

$x \geq 1$

Therefore

$x \in[1,4]$