Question

If $|x-1|+|x-4|=4$, then $x\in$

• A. $\{-\frac{1}{2},\frac{9}{2}\}$
• B. $\{\frac{1}{2},\frac{9}{2}\}$
• C. $\{-\frac{9}{2},\frac{1}{2}\}$
• D. $\{-\frac{9}{2},-\frac{1}{2}\}$

Answer 1

The correct option is B $\{\frac{1}{2},\frac{9}{2}\}$

If $x<1$,
$-x+1-x+4=4$
$\Rightarrow x=\frac{1}{2}$

If $1\le x<4$,
$x-1-x+4=4$
$\Rightarrow 3=4$ (Not possible)

If $x\ge 4$,
$x-1+x-4=4$
$\Rightarrow x=\frac{9}{2}$

$\therefore x=\frac{1}{2},\frac{9}{2}$