What is the answer to |x|+|x+1|=1 ?

The answer to |x|+|x+1|=1 is -1<= x<= 0

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|x|+|x+1|=1

∣ x ∣ + ∣ x + 1 ∣ = 1

- 1 \leq x \leq 0

Solution steps

∣ x ∣ + ∣ x + 1 ∣ = 1

Find positive and negative intervals

x < - 1, - 1 \leq x < 0, x \geq 0

Solve the inequality for each interval

No Solution or - 1 \leq x < 0 or x = 0

Merge Overlapping Intervals

- 1 \leq x \leq 0

x^{2} + x - 4 = x^{2} - 4 + ∣ x ∣

∣ x - 1 ∣ + ∣ 3 x + 6 ∣ = 7

∣ 7 x - 12 ∣ - ∣ 7 x - 11 ∣ = 1

x^{2} - 2 x - 8 = 2 x

∣ x - 2 ∣ + ∣ x - 4 ∣ = 6