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

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

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|3x-5|=x+1

∣ 3 x - 5 ∣ = x + 1

x = 1 or x = 3

Solution steps

∣ 3 x - 5 ∣ = x + 1

Find positive and negative intervals

x < \frac{5}{3}, x \geq \frac{5}{3}

Solve the inequality for each interval

x = 1 or x = 3

∣ k + 6 ∣ = 9

3 ∣ x - 6 ∣ = 16

∣ 3 - 5 x ∣ = 7

∣ 3 x - 11 ∣ = x + 3

∣ - 3 x - 1 ∣ + 6 = 4