Solve each of the following in equations and represent the solution set on the number line.
$5-2 x \mid \leq 3, x \in R$
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
$x \in[1,4]$
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