What is the answer to |x-1|=-3x ?

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

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|x-1|=-3x

∣ x - 1 ∣ = - 3 x

x = - \frac{1}{2}

Decimal Notation

x = - 0.5

Solution steps

∣ x - 1 ∣ = - 3 x

Find positive and negative intervals

x < 1, x \geq 1

Solve the inequality for each interval

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

x = - \frac{1}{2}

2 \cdot ∣ x - 2 ∣ - 3 \cdot ∣ 2 x + 4 ∣ = 5 - 2 \cdot (1 - 3 x)

∣ 2 x - 1 ∣ = x + 1

x^{2} - 1 + ∣ x ∣ = 2

3 - 2 ∣ x + 1 ∣ = 1

(x^{2} + ∣ x - 1 ∣) = x (x + 2)