Find the number of real solutions of |x – 1| = |x – 2| + |x

Engineering

Mathematics

Properties of Logarithm

Question

Find the number of real solutions of |x – 1| = |x – 2| + |x – 3|.

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Case-I: x $\leq$ 1 , 1 – x = 2 – x + 3 – x
x = 4 (rejected)
Case-II: 1 < x $\leq$ 2 , x – 1 = 2 –x + 3 – x

x = 2

Case-III: 2 < x < 3, x – 1 = x – 2 + 3 – x

x = 2

Case-IV: x $\geq$ 3, x – 1 = x – 2 + x – 2

x = 4
$∴$ x = 2, 4