What is the answer to |x-2|=3x+1 ?

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

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|x-2|=3x+1

∣ x - 2 ∣ = 3 x + 1

x = \frac{1}{4}

Solution steps

∣ x - 2 ∣ = 3 x + 1

Find positive and negative intervals

x < 2, x \geq 2

Solve the inequality for each interval

x = \frac{1}{4} or No Solution

x = \frac{1}{4}

\frac{5 ^{6}}{5}

\frac{1}{3} x - \frac{5}{6} = - \frac{2}{3}

e^{- 2 l n (4)}

\frac{- x ^{2} + 6 x - 8}{x ^{3} ∣ x - 2 ∣} = 0

2 (x + 4)^{2} = 6