What is the answer to |x-4|-|x|=4 ?

The answer to |x-4|-|x|=4 is x<= 0

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|x-4|-|x|=4

∣ x - 4 ∣ - ∣ x ∣ = 4

x \leq 0

Solution steps

∣ x - 4 ∣ - ∣ x ∣ = 4

Find positive and negative intervals

x < 0, 0 \leq x < 4, x \geq 4

Solve the inequality for each interval

x < 0 or x = 0 or No Solution

Merge Overlapping Intervals

x \leq 0

∣ 3 x + 1 ∣ = ∣ x - 3 ∣

- 2 ∣ 5 - 4 x ∣ + 5 = - 1

∣ 4 x + 3 ∣ = 0

∣ x - 5 ∣ + ∣ x - 8 ∣ = 14

∣ x - 1 ∣ + 2 = 4