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Choose the option which represents the solution of the equation given below-

$3 (y − 5) 4 − 4 y = 3 − (y − 3) 2$

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y = -3

y = 3

y = 2

y = 5

answer is A.

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Detailed Solution

The given linear equation is as follows,

3 (y − 5) 4 − 4 y = 3 − (y − 3) 2

.
We first multiply each side of the given equation by 4 and simplify.

3 (y − 5) 4 (4) − 4 y (4) = 3 (4) − (y − 3) 2 (4) 3 (y − 5) − 16 y = 12 − 2 (y − 3)

3 (y) + 3 (− 5) − 16 y = 12 − 2 (y) − 2 (− 3) 3 y − 15 − 16 y = 12 − 2 y + 6 − 13 y − 15 = 18 − 2 y

Adding 15 on both sides, we get,

− 13 y − 15 + 15 = 18 − 2 y + 15 − 13 y = 33 − 2 y

Adding

2 y

on both sides, we get,

− 13 y + 2 y = 33 − 2 y + 2 y − 11 y = 33

Dividing by -11 on both sides, we get,

− 11 y − 11 = 33 − 11 y = − 3

So, the value of the variable y is -3.
Hence the correct option is (1).

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