What is the answer to 1/2 |z-3|-5=-2 ?

The answer to 1/2 |z-3|-5=-2 is z=-3\lor z=9

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1/2 |z-3|-5=-2

\frac{1}{2} ∣ z - 3 ∣ - 5 = - 2

z = - 3 or z = 9

Solution steps

\frac{1}{2} ∣ z - 3 ∣ - 5 = - 2

Move

5

to the right side

\frac{1}{2} ∣ z - 3 ∣ = 3

Multiply both sides by

2

∣ z - 3 ∣ = 6

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

z - 3 = - 6 or z - 3 = 6

z - 3 = - 6 or z - 3 = 6

z = - 3 or z = 9

∣ 3 x + 5 ∣ = 5 x + 11

3 ∣ x - 9 ∣ = ∣ - 4 x + 8 ∣

22 = ∣ 4 x + 10 ∣

∣ x - 1 ∣ = 19

\frac{∣ x - 5 ∣}{8} = 5

What is the answer to 1/2 |z-3|-5=-2 ?
The answer to 1/2 |z-3|-5=-2 is z=-3\lor z=9
Solve for z: 1/2 |z-3|-5=-2
The solution is z=-3\lor z=9