What is |5-x|+|x-13|<|2-x| ?

The solution to |5-x|+|x-13|<|2-x| is 10<x<16

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|5-x|+|x-13|<|2-x|

∣ 5 - x ∣ + ∣ x - 13 ∣ < ∣ 2 - x ∣

10 < x < 16

Solution steps

∣ 5 - x ∣ + ∣ x - 13 ∣ < ∣ 2 - x ∣

Find positive and negative intervals

x \leq 2, 2 < x \leq 5, 5 < x < 13, x \geq 13

Solve the inequality for each interval

No Solution or 10 < x < 13 or 13 \leq x < 16

Merge Overlapping Intervals

10 < x < 16

∣ x ∣ + ∣ x - 4 ∣ > 4

(b) ∣ x + 2 ∣ + 2 \geq 0

\frac{( 3 x + 6 )}{9} \geq 5

4 ∣ x - 9 ∣ > 16

x^{2} - ∣ 5 x + 6 ∣ > 0