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

The answer to |z|+|z-4|=6 is z=-1\lor z=5

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|z|+|z-4|=6

∣ z ∣ + ∣ z - 4 ∣ = 6

z = - 1 or z = 5

Solution steps

∣ z ∣ + ∣ z - 4 ∣ = 6

Find positive and negative intervals

z < 0, 0 \leq z < 4, z \geq 4

Solve the inequality for each interval

z = - 1 or No Solution or z = 5

z = - 1 or z = 5

∣ x + 2 ∣ = ∣ 2 x - 3 ∣

2 x - x^{2} - 3 = 1

(x - 1) x^{2} - 4 x + 3 + 2 x^{2} + 3 x - 5 = 0

∣ 2 x - 1 ∣ = ∣ x + 3 ∣

- 2 x^{2} - 8 x = 10