Solve the equation. \[ 0.5 x+\frac{8}{7} x=x+9 \]

Step 1 ：Combine like terms on the left side of the equation to get \(1.64285714285714x\).

Step 2 ：Subtract x from both sides of the equation to get \(0.64285714285714x = 9\).

Step 3 ：Divide both sides of the equation by \(0.64285714285714\) to solve for x.

Step 4 ：The solution to the equation is \(\boxed{14}\).

Step 5 ：Substitute x = 14 into the original equation to check the solution. The left side of the equation equals the right side, so the solution is correct.