## Quant Question Of The Day: 98

# Algebra

**How many real numbers x are solutions to the following equation ?**

**|x − 1| = |x − 2| + |x − 3|**

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Quant question of the day, Question of the day

**How many real numbers x are solutions to the following equation ?**

**|x − 1| = |x − 2| + |x − 3|**

**If x < 1, the equation becomes (1 – x) = (2 – x) + (3 – x) which simplifies to x = 4, contradicting the assumption the assumption x < 1. If 1 < x < 2, we get (x – 1) = (2 – x) + (3 – x), which gives x = 2. If 2 ≤ x ≤ 3, we get (x – 1) = (x – 2) + (3 – x), which again gives x = 2. If x ≥ 3, we get (x – 1) = (x – 2) + (x – 3), or x = 4. So 2 and 4 are the only solutions, and the answer is 2.**

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2 values of x

X= 2 and 4

x=2&4

2