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 ∣ \geq 6

x \leq 0 or x \geq 6

Solution steps

∣ x - 2 ∣ + ∣ x - 4 ∣ \geq 6

Find positive and negative intervals

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

Solve the inequality for each interval

x \leq 0 or No Solution or x \geq 6

Merge Overlapping Intervals

x \leq 0 or x \geq 6

∣ x - 3 ∣ + ∣ x + 4 ∣ \geq 12

x^{2} - 2 x + ∣ x - 4 ∣ > x^{2} - 3 x + 4

x^{2} - 4 x < 5

x^{2} - 5 x < 6

x^{2} - 2 x < x