What is the answer to |x-1|=2|x-4| ?

The answer to |x-1|=2|x-4| is x=3\lor x=7

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|x-1|=2|x-4|

∣ x - 1 ∣ = 2 ∣ x - 4 ∣

x = 3 or x = 7

Solution steps

∣ x - 1 ∣ = 2 ∣ x - 4 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or x = 3 or x = 7

x = 3 or x = 7

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

\frac{3}{4} x^{2} - \frac{2}{5} x = \frac{4}{5} x^{2} + \frac{3}{4}

8 x + 18 = 50

2 {3 z - (4 z + 3)} = 3 z + 4

x^{2} - 3 x < 40