What is the answer to |4x+9|-6=x ?

The answer to |4x+9|-6=x is x=-3\lor x=-1

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|4x+9|-6=x

∣ 4 x + 9 ∣ - 6 = x

x = - 3 or x = - 1

Solution steps

∣ 4 x + 9 ∣ - 6 = x

Find positive and negative intervals

x < - \frac{9}{4}, x \geq - \frac{9}{4}

Solve the inequality for each interval

x = - 3 or x = - 1

x, ∣ 5 x - 2 ∣ = 8

∣ 4 - 3 x ∣ = 10

- 2 ∣ 3 - x ∣ = - 8

- 2 ∣ 8 - x ∣ - 6 = - 12

- 4 ∣ x - 2 ∣ - 9 = - 37