Question

If $|2x-1|+|2x-2|=6$, then $x\in$

• A. $\{-\frac{3}{4},\frac{9}{4}\}$
• B. $\{\frac{9}{4},6\}$
• C. $\{\frac{3}{4},\frac{9}{4}\}$
• D. $\{-\frac{3}{4},\frac{9}{4},6\}$

Answer 1

The correct option is A $\{-\frac{3}{4},\frac{9}{4}\}$

$|2x-1|+|2x-2|=6$
If $x<\frac{1}{2}$,
$-2x+1-2x+2=6$
$\Rightarrow -4x=3\Rightarrow x=\frac{-3}{4}$

If $\frac{1}{2}\le x<1$,
$2x-1-2x+2=6$
$\Rightarrow 1=6$ which is absurd.

If $x\ge 1$,
$2x-1+2x-2=6\Rightarrow x=\frac{9}{4}$

$\therefore x=-\frac{3}{4},\frac{9}{4}$