What is the answer to |7x-1|=2x+19 ?

The answer to |7x-1|=2x+19 is x=-2\lor x=4

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|7x-1|=2x+19

∣ 7 x - 1 ∣ = 2 x + 19

x = - 2 or x = 4

Solution steps

∣ 7 x - 1 ∣ = 2 x + 19

Find positive and negative intervals

x < \frac{1}{7}, x \geq \frac{1}{7}

Solve the inequality for each interval

x = - 2 or x = 4

∣ 2 x + 5 ∣ - 10 = 7

7 ∣ x - 2 ∣ = 8

∣ x - 2 ∣ = 6 x + 8

∣ x - 7 ∣ = 3 x + 2

- 2 ∣ x + 1 ∣ = 4