Question

Solve for x and simplify the answer fully.

x+6/x-5=5/4

Answer 1

To solve the equation

\[
\frac{x + 6}{x - 5} = \frac{5}{4},
\]

we start by cross-multiplying to eliminate the fractions. This gives us:

\[
4(x + 6) = 5(x - 5).
\]

Now, distribute both sides:

\[
4x + 24 = 5x - 25.
\]

Next, we want to isolate \(x\). First, subtract \(4x\) from both sides:

\[
24 = 5x - 4x - 25,
\]
which simplifies to

\[
24 = x - 25.
\]

Now, add 25 to both sides:

\[
24 + 25 = x,
\]

thus,

\[
x = 49.
\]

Therefore, the solution to the equation is

\[
\boxed{49}.
\]