What is the answer to |x-4|-|x+4|=8 ?

The answer to |x-4|-|x+4|=8 is x<=-4

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|x-4|-|x+4|=8

∣ x - 4 ∣ - ∣ x + 4 ∣ = 8

x \leq - 4

Solution steps

∣ x - 4 ∣ - ∣ x + 4 ∣ = 8

Find positive and negative intervals

x < - 4, - 4 \leq x < 4, x \geq 4

Solve the inequality for each interval

x < - 4 or x = - 4 or No Solution

Merge Overlapping Intervals

x \leq - 4

∣ 12 + 3 b ∣ = - 3

∣ x ∣ + ∣ x + 1 ∣ = 1

x^{2} + x - 4 = x^{2} - 4 + ∣ x ∣

∣ x - 1 ∣ + ∣ 3 x + 6 ∣ = 7

∣ 7 x - 12 ∣ - ∣ 7 x - 11 ∣ = 1