What is the answer to 1=4-|9-2v| ?

The answer to 1=4-|9-2v| is v=3\lor v=6

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1=4-|9-2v|

1 = 4 - ∣ 9 - 2 v ∣

v = 3 or v = 6

Solution steps

1 = 4 - ∣ 9 - 2 v ∣

Move

∣ 9 - 2 v ∣

to the left side

1 + ∣ 9 - 2 v ∣ = 4

Move

1

to the right side

∣ 9 - 2 v ∣ = 3

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

9 - 2 v = - 3 or 9 - 2 v = 3

9 - 2 v = - 3 or 9 - 2 v = 3

v = 3 or v = 6

7 - 2 ∣ 3 x + 6 ∣ = 3

- 2 ∣ 3 x + 4 ∣ + 5 = - 7

500 = ∣ 5 q - 500 ∣

∣ x + 7 ∣ = \frac{1}{2}

∣ y + 2 ∣ + 4 = 7