What is the answer to 2|z|=|z-2| ?

The answer to 2|z|=|z-2| is z=-2\lor z= 2/3

Solve for z: 2|z|=|z-2|

The solution is z=-2\lor z= 2/3

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2 ∣ z ∣ = ∣ z - 2 ∣

z = - 2 or z = \frac{2}{3}

Decimal

z = - 2, z = 0.66666 \dots

Solution steps

2 ∣ z ∣ = ∣ z - 2 ∣

Find positive and negative intervals

z < 0, 0 \leq z < 2, z \geq 2

Solve the inequality for each interval

z = - 2 or z = \frac{2}{3} or No Solution

z = - 2 or z = \frac{2}{3}

5 - ∣ r + 1 ∣ = 9

\frac{∣ w + 9 ∣}{7} = 2

8 + ∣ 7 + 4 x ∣ = 14

∣ 4 x - 2 ∣ + 10 = 16

10 ∣ 2 x - 1 ∣ + 9 = 59