What is the answer to |x-12|= x/3 ?

The answer to |x-12|= x/3 is x=9\lor x=18

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|x-12|= x/3

∣ x - 12 ∣ = \frac{x}{3}

x = 9 or x = 18

Solution steps

∣ x - 12 ∣ = \frac{x}{3}

Find positive and negative intervals

x < 12, x \geq 12

Solve the inequality for each interval

x = 9 or x = 18

x^{2} - 7 x = 18

∣ 2 x - 1 ∣ = 8 x

x^{2} - 20 x - 18 = 7

\frac{∣ 2 x - 1 ∣}{x + 1} \leq 2

10 = - 5 (x - 4)