What is the answer to 9=|z+2|+8 ?

The answer to 9=|z+2|+8 is z=-3\lor z=-1

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9=|z+2|+8

9 = ∣ z + 2 ∣ + 8

z = - 3 or z = - 1

Solution steps

9 = ∣ z + 2 ∣ + 8

Switch sides

∣ z + 2 ∣ + 8 = 9

Move

8

to the right side

∣ z + 2 ∣ = 1

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

z + 2 = - 1 or z + 2 = 1

z + 2 = - 1 or z + 2 = 1

z = - 3 or z = - 1

- 89 = - ∣ 8 v - 80 ∣ - 9

∣ 2 x - 3 ∣ = 5 - 4 x

∣ x ∣ + 1 = 67

∣ a - 2 ∣ = 0

9 - ∣ 6 x ∣ = 7