What is the answer to |x-1|=|x+4| ?

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

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|x-1|=|x+4|

∣ x - 1 ∣ = ∣ x + 4 ∣

x = - \frac{3}{2}

Decimal Notation

x = - 1.5

Solution steps

∣ x - 1 ∣ = ∣ x + 4 ∣

Find positive and negative intervals

x < - 4, - 4 \leq x < 1, x \geq 1

Solve the inequality for each interval

No Solution or x = - \frac{3}{2}

x = - \frac{3}{2}

x^{2} + x + 2 - x^{2} - x + 1 = ∣ 2 x + 1 ∣

\frac{x}{2 + 3} \cdot (5 - 6 x) + (12 x - 2) \frac{x}{4 + 3} = 0

x^{2} - 4 x - 20 = 1

∣ 2 x + 1 ∣ - 2 ∣ x - 2 ∣ = 5

∣ x - 1 ∣ + ∣ x - 4 ∣ = 3