What is the answer to |x|+|x+5|=5 ?

The answer to |x|+|x+5|=5 is -5<= x<= 0

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|x|+|x+5|=5

∣ x ∣ + ∣ x + 5 ∣ = 5

- 5 \leq x \leq 0

Solution steps

∣ x ∣ + ∣ x + 5 ∣ = 5

Find positive and negative intervals

x < - 5, - 5 \leq x < 0, x \geq 0

Solve the inequality for each interval

No Solution or - 5 \leq x < 0 or x = 0

Merge Overlapping Intervals

- 5 \leq x \leq 0

∣ x - 8 ∣ = 3 x^{2} - 5 - ∣ 2 x + 3 ∣

3 ∣ x + 2 ∣ - x = 3

∣ x - 5 ∣^{2} + ∣ x - 5 ∣ - 24 = 0

1 x^{2} - x + ∣ x + 1 ∣ = 5

∣ 3 x + 2 ∣ = x + 1, ∣ 2 x - 3 ∣ = x - 5, ∣ 3 x - 2 ∣ = 2 x + 3