Question

Number of integral values of $x$ satisfying the equation $\left|x^2-3x-4\right|+\left|x^2-5x-6\right|=|2x+2|$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (D)

$\left|x^2-3x-4\right|+\left|x^2-5x-6\right|=|2x+2|$

$=\left|\left(x^2-3x-4\right)-\left(x^2-5x-6\right)\right|$
$|x|+|y|=|x-y|\text{ is true if }xy\le 0$
$\Rightarrow \left(x^2-3x-4\right)\left(x^2-5x-6\right)\le 0$
$\Rightarrow (x-4)(x+1)(x-6)(x+1)\le 0$
$x\in \{-1\}\cup [4,6]$