What is the answer to |x-1|-|4-x|=0 ?

The answer to |x-1|-|4-x|=0 is x= 5/2

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|x-1|-|4-x|=0

∣ x - 1 ∣ - ∣ 4 - x ∣ = 0

x = \frac{5}{2}

Decimal

x = 2.5

Solution steps

∣ x - 1 ∣ - ∣ 4 - x ∣ = 0

Find positive and negative intervals

x < 1, 1 \leq x \leq 4, x > 4

Solve the inequality for each interval

No Solution or x = \frac{5}{2}

x = \frac{5}{2}

y, x = 2 ∣ y ∣ - 3

54 = ∣ a - 2 ∣

\frac{6 x - 5}{4} = 7

∣ 2 x - 5 ∣ = 6 x + 11

\frac{2 x}{3} + 5 = - 8