Question

Write the solution of $|x-\frac{5}{2}|=\frac{3}{2}$

Answer 1

Simplifying $\left|x-\frac{5}{2}\right|=\frac{3}{2}$

$x-\frac{5}{2}=\pm \frac{3}{2}$

Taking $+\frac{3}{2}$,

$x-\frac{5}{2}=\frac{3}{2}$

$x=\frac{3}{2}+\frac{5}{2}$

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

$x=4$

Taking $-\frac{3}{2}$,

$x-\frac{5}{2}=-\frac{3}{2}$

$x=-\frac{3}{2}+\frac{5}{2}$

$x=\frac{2}{2}$

$x=1$

Therefore, $x=1,4$.