What is |x-2|<= |x-4| ?

The solution to |x-2|<= |x-4| is x<= 3

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|x-2|<= |x-4|

∣ x - 2 ∣ \leq ∣ x - 4 ∣

x \leq 3

Solution steps

∣ x - 2 ∣ \leq ∣ x - 4 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

x < 2 or 2 \leq x \leq 3 or No Solution

Merge Overlapping Intervals

x \leq 3

∣ 2 x - 1 ∣ > x + 1

∣ 2 x + 1 ∣ > x + 5

∣ x - 8 ∣ > 1

5 \leq \frac{1 + x}{3}

∣ x - 1 ∣ + ∣ 2 x - 4 ∣ + ∣ 3 x - 9 ∣ < 5