What is the answer to |x-2|+|x+6|=8 ?

The answer to |x-2|+|x+6|=8 is -6<= x<= 2

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|x-2|+|x+6|=8

∣ x - 2 ∣ + ∣ x + 6 ∣ = 8

- 6 \leq x \leq 2

Solution steps

∣ x - 2 ∣ + ∣ x + 6 ∣ = 8

Find positive and negative intervals

x < - 6, - 6 \leq x < 2, x \geq 2

Solve the inequality for each interval

No Solution or - 6 \leq x < 2 or x = 2

Merge Overlapping Intervals

- 6 \leq x \leq 2

x^{2} + 1 = x^{2} - 3 x

∣ x - 3 ∣ = 4 - x

(3 x - 2) 2 - 5 ∣ 3 x - 2 ∣ - 6 = 0

∣ x - 4 ∣ - ∣ x ∣ = 4

∣ 3 x + 1 ∣ = ∣ x - 3 ∣