What is the answer to |x-5|-|2+x|=4 ?

The answer to |x-5|-|2+x|=4 is x=-1/2

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|x-5|-|2+x|=4

∣ x - 5 ∣ - ∣ 2 + x ∣ = 4

x = - \frac{1}{2}

Decimal Notation

x = - 0.5

Solution steps

∣ x - 5 ∣ - ∣ 2 + x ∣ = 4

Find positive and negative intervals

x < - 2, - 2 \leq x < 5, x \geq 5

Solve the inequality for each interval

No Solution or x = - \frac{1}{2}

x = - \frac{1}{2}

5 x^{2} - 3 = 2

3 x^{2} - 4 x^{2} - 1 + x - 1 = 0

∣ x - 2 ∣ + ∣ x - 5 ∣ = 3

∣ x - 1 ∣ - ∣ x ∣ + ∣ x + 1 ∣ = 2

∣ x - 1 ∣ = 2 x - 5