What is the answer to |3x-1|=|x+5| ?

The answer to |3x-1|=|x+5| is x=-1\lor x=3

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|3x-1|=|x+5|

∣ 3 x - 1 ∣ = ∣ x + 5 ∣

x = - 1 or x = 3

Solution steps

∣ 3 x - 1 ∣ = ∣ x + 5 ∣

Find positive and negative intervals

x < - 5, - 5 \leq x < \frac{1}{3}, x \geq \frac{1}{3}

Solve the inequality for each interval

No Solution or x = - 1 or x = 3

x = - 1 or x = 3

∣ x + 1 ∣ = 2 x + 1

x (7 x - 5) = 12

6 x^{2} - 9 x + 2 = 0

4 (6 x - 10) = 8 x + 40

\frac{1}{2} x + 5 = \frac{3}{10} x