What is the answer to |x-1|-|2x-5|=2x ?

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

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|x-1|-|2x-5|=2x

∣ x - 1 ∣ - ∣ 2 x - 5 ∣ = 2 x

x = - 4

Solution steps

∣ x - 1 ∣ - ∣ 2 x - 5 ∣ = 2 x

Find positive and negative intervals

x < 1, 1 \leq x < \frac{5}{2}, x \geq \frac{5}{2}

Solve the inequality for each interval

x = - 4 or No Solution

x = - 4

x^{2} - 3 ∣ x ∣ + 2 = 0

3 ∣ 1 - 2 x ∣ - 9 = 0

∣ 3 (x - 4) ∣ = 9

∣ 2 (x - 2) ∣ = \frac{5}{2}

∣ x + 1 ∣ = 5