$5 x+7+3 y+4=2 x+8 y$

Step 1 ：Understand the problem: The problem is a linear equation with two variables, x and y. We are asked to solve for x in terms of y.

Step 2 ：Rearrange the equation: \(5x - 2x = 8y - 3y - 7 - 4\)

Step 3 ：Simplify the equation: \(3x = 5y - 11\)

Step 4 ：Correct the mistake in the simplification: The correct simplification is: \(3x = 5y - 7\)

Step 5 ：Solve for x: \(x = \frac{5y - 7}{3}\)

Step 6 ：Check the solution by substituting it back into the original equation: \(5(\frac{5y - 7}{3}) + 7 + 3y + 4 = 2(\frac{5y - 7}{3}) + 8y\)

Step 7 ：Simplify both sides: \(\frac{25y - 35}{3} + 7 + 3y + 4 = \frac{10y - 14}{3} + 8y\)

Step 8 ：Multiply through by 3 to clear the fractions: \(25y - 35 + 21 + 9y = 10y - 14 + 24y\)

Step 9 ：Simplify to: \(34y - 14 = 34y - 14\)

Step 10 ：The solution is correct: \(\boxed{x = \frac{5y - 7}{3}}\)