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If $7 y + 4 y + 2 = − 43$ , then y=[[1]].

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answer is − 4 5.

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Detailed Solution

7 y + 4 y + 2 = − 43

, then y =

− 45

.
The given linear equation is as follows,

7 y + 4 y + 2 = − 43

.
We first need to eliminate the denominators on both sides of the equation. To do so, we will cross-multiply the denominators with the numerators on the either side as follows and simplify.

3 (7 y + 4) = − 4 (y + 2)

3 (7 y) + 3 (4) = − 4 (y) − 4 (2) 21 y + 12 = − 4 y − 8

Subtracting 12 on both sides, we get,

21 y + 12 − 12 = − 4 y − 8 − 12 21 y = − 4 y − 20

Adding

4 y

on both sides, we get,

21 y + 4 y = − 4 y + 4 y − 20 25 y = − 20

Dividing by 25 on both sides, we get,

25 y 25 = − 20 25 y = − 45

So, the value of the variable y is

− 45

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