CAT 2022 Slot 1 QA Question 4: The largest real value of $a$ for which the equation $|x + a| + |x - 1| = 2$ has an infinite number of solutions for $x$ is

Question

The largest real value of $a$ for which the equation $|x + a| + |x - 1| = 2$ has an infinite number of solutions for $x$ is

Accepted Answer

The expression is the sum of the distances of $x$ from the two points $-a$ and $1$ on the number line.
For infinitely many values of $x$, the sum of distances must be constant on the whole interval between these two points. That constant is the distance between the two points.
$|1 - (-a)| = 2$
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The largest real value of aaa for which the equation ∣x+a∣+∣x−1∣=2|x + a| + |x - 1| = 2∣x+a∣+∣x−1∣=2 has an infinite number of solutions for xxx is

The largest real value of $a$ for which the equation $|x + a| + |x - 1| = 2$ has an infinite number of solutions for $x$ is