CAT 2022 Slot 1 Paper

In the question, it is given that the equation $\left|\mathit{x}+\mathit{a}\right|+|\mathit{x}-1|=2$ has an infinite number of solutions for any value of $\mathit{x}$
This is possible when $\mathit{x}$ in $\left|\mathit{x}+\mathit{a}\right|$ and $\mathit{x}$ in $\left|\mathit{x}-1\right|$ cancels out.
Case 1:

$-\mathit{a}-\mathit{x}+\mathit{x}-1=2$
$\mathit{a}=-3$
Case 2:
$\mathit{x}+\mathit{a}\ge 0$ and
$\mathit{x}+\mathit{a}-\mathit{x}+1=2$
$\mathit{a}=1$
Largest value of $\mathit{a}$ is 1.
The answer is option C.