What is |x-2|+|x-4|>6 ?

The solution to |x-2|+|x-4|>6 is x 6

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|x-2|+|x-4|>6

∣ x - 2 ∣ + ∣ x - 4 ∣ > 6

x < 0 or x > 6

Interval Notation

(- \infty, 0) \cup (6, \infty)

Solution steps

∣ x - 2 ∣ + ∣ x - 4 ∣ > 6

Find positive and negative intervals

x < 2, 2 \leq x < 4, x \geq 4

Solve the inequality for each interval

x < 0 or No Solution or x > 6

Merge Overlapping Intervals

x < 0 or x > 6

x^{2} - ∣ 3 x + 2 ∣ + x \geq 0

\frac{x + 5}{∣ 1 - x ∣} > 1

∣ 2 x - 10 ∣ > 10

∣ x ∣^{x^{2} - x - 2} < 1

∣ 5 x - 2 ∣ \leq ∣ 3 x + 5 ∣