Solve and check the linear equation.
\[
27-\frac{x}{4}=\frac{x}{5}
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is (Type an integer or a simplified fraction.)
B. The solution set is $\{x \mid x$ is a real number $\}$.
C. The solution set is $\varnothing$.
Answer
Final Answer: The solution set is \(\boxed{60}\).
Step 1 ：Multiply every term by 20 to get rid of the fractions: \(20(27-\frac{x}{4})=20(\frac{x}{5})\), which simplifies to \(540-5x=4x\).
Step 2 ：Move all terms involving x to one side and constant terms to the other side: \(540=9x\).
Step 3 ：Simplify the equation and solve for x: \(x=\frac{540}{9}=60\).
Step 4 ：Check the solution by substituting x = 60 back into the original equation: \(27-\frac{60}{4}=\frac{60}{5}\), which simplifies to \(27-15=12\), and since both sides of the equation are equal, the solution is correct.
Step 5 ：Final Answer: The solution set is \(\boxed{60}\).
