Question

The total number of integral solution(s) of $|4x-5|+|6x-12|=|2x-7|$ is/are

• A. $2$
• B. $1$
• C. $3$
• D. $0$

Answer 1

The correct option is B $1$

$|4x-5|+|6x-12|=|2x-7|$
We know that $|a-b|=|a|+|b|$, then $ab\le 0$
Here, $2x-7=(6x-12)-(4x-5)$
So,
$(6x-12)(4x-5)\le 0\Rightarrow (x-2)(x-\frac{5}{4})\le 0$
$\therefore x\in [\frac{5}{4},2]$
Hence, there is only $1$ integer solution i.e $x=2$