What is the answer to |x-1|+|x+5|=6 ?

The answer to |x-1|+|x+5|=6 is -5<= x<= 1

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|x-1|+|x+5|=6

∣ x - 1 ∣ + ∣ x + 5 ∣ = 6

- 5 \leq x \leq 1

Solution steps

∣ x - 1 ∣ + ∣ x + 5 ∣ = 6

Find positive and negative intervals

x < - 5, - 5 \leq x < 1, x \geq 1

Solve the inequality for each interval

No Solution or - 5 \leq x < 1 or x = 1

Merge Overlapping Intervals

- 5 \leq x \leq 1

∣ - 2 x + 8 ∣ = 0

∣ 2 - x ∣ = ∣ x + 5 ∣

4 ∣ 2 x - 5 ∣ = 30 + 3 x

∣ x ∣ + ∣ y ∣ = 0

6 ∣ x - 2 ∣ - 4 ∣ 3 - x ∣ + 17 = 0