What is |x-1|<|x-2|+|x-3| ?

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|x-1|<|x-2|+|x-3|

∣ x - 1 ∣ < ∣ x - 2 ∣ + ∣ x - 3 ∣

x < 2 or x > 4

Interval Notation

(- \infty, 2) \cup (4, \infty)

Solution steps

∣ x - 1 ∣ < ∣ x - 2 ∣ + ∣ x - 3 ∣

Find positive and negative intervals

x < 1, 1 \leq x < 2, 2 \leq x < 3, x \geq 3

Solve the inequality for each interval

x < 1 or 1 \leq x < 2 or No Solution or x > 4

Merge Overlapping Intervals

x < 2 or x > 4

\frac{8 ! 4 !}{7 ! 2 !}

15 - 9

7 (x + 2) = 7 x - 10

x^{2} - 3 3^{2}

\frac{4 x ^{2} + 2 x - 6}{3 x + 1} < 3 x + 1