First I'll make the assumption that you mean
4x+5
f(x) = ------------
x+4
and then set this function = to 25/9:
4x+5 25
f(x) = ------------ = ------
x+4 9
Solve for x: Cross-multiplying, we get 36x + 45 = 25x + 100.
Consolidating like terms, we get 11x = 55. Thus, x = 5.
x = 5
equate f(x) = [tex]\frac{25}{9}[/tex]
[tex]\frac{4x + 5}{x + 4}[/tex] = [tex]\frac{25}{9}[/tex] → (cross- multiply)
9(4x + 5) = 25(x + 4) → (distribute both sides )
36x + 45 = 25x + 100 → ( subtract 25x from both sides )
11x + 45 = 100 → ( subtract 45 from both sides )
11x = 55 → ( divide both sides by 11 )
x = [tex]\frac{55}{11}[/tex] = 5
