Bot GPT 4-o mini 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
\[ \boxed{49}. \]
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