What is the answer to |3x-7|=x+3 ?

The answer to |3x-7|=x+3 is x=1\lor x=5

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|3x-7|=x+3

∣ 3 x - 7 ∣ = x + 3

x = 1 or x = 5

Solution steps

∣ 3 x - 7 ∣ = x + 3

Find positive and negative intervals

x < \frac{7}{3}, x \geq \frac{7}{3}

Solve the inequality for each interval

x = 1 or x = 5

x^{2} + 3 ∣ x - 1 ∣ = 0

∣ 3 x - 2 ∣ + 4 = 10

∣ 3 x ∣ + 5 = 20

7 ∣ k + 2 ∣ + 8 = 15

∣ 3 x - 7 ∣ - 9 = - 4