Find the solution of $2 x − (7 − 5 x) 9 x − (3 + 4 x) = 76$ , and select the option which follows.

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x=5

x=6

x=4

x=3

answer is A.

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Detailed Solution

The given linear equation is as follows,

2 x − (7 − 5 x) 9 x − (3 + 4 x) = 76

.
We cross-multiply the denominators with the numerators on the either side as follows,

6 {2 x − (7 − 5 x)} = 7 {9 x − (3 + 4 x)} 6 {2 x − 7 + 5 x} = 7 {9 x − 3 − 4 x} 6 {7 x − 7} = 7 {5 x − 3} 6 (7 x) + 6 (− 7) = 7 (5 x) + 7 (− 3) 42 x − 42 = 35 x − 21

42 x − 35 x − 42 = 35 x − 35 x − 21 7 x − 42 = − 21

7 x − 42 + 42 = − 21 + 42 7 x = 21

7 x 7 = 217 x = 3

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

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