What is the answer to |x|+|x+2|=4 ?

The answer to |x|+|x+2|=4 is x=-3\lor x=1

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|x|+|x+2|=4

∣ x ∣ + ∣ x + 2 ∣ = 4

x = - 3 or x = 1

Solution steps

∣ x ∣ + ∣ x + 2 ∣ = 4

Find positive and negative intervals

x < - 2, - 2 \leq x < 0, x \geq 0

Solve the inequality for each interval

x = - 3 or No Solution or x = 1

x = - 3 or x = 1

∣ x ∣ + ∣ x + 2 ∣ = 3

x^{2} - 2 ∣ x ∣ = 8

∣ x ∣ + ∣ x + 2 ∣ = 2

∣ x - 2 ∣ + ∣ x - 5 ∣ = 7

∣ x + 5 ∣ = - 7