Excellent work by Justin L.
yielding (5x+20)/4 = 5(x+4)/4
Wolfram Alpha conveniently plots the initial equation and it's inverse and the Identity or y=x (y=1x + 0) Which is also another check. Both equations should be mirror images about the y=x.
This will really be more fun when you do this with quadratic equations.
Hint: Get a small mirror (like cosmetic size) and stand it on the y=x line and look at the
mirror from an angle ... you will see the reflection ... meaning you can trace the inverse
You can check your answer algebraically (in addition to the above graphical method) by computing the composite function. if your original function is f(x) = (4x-10)/5 and your inverse is g(x)=5x+20)/4 then
y = f(g(x) = g(f(x) = x the Identity y=x
so let f(x) = (4x-20)/5 and g(x) = (5x+20)/4
let us do f(g(x))
which says use f(x) but where you see x substitute the full g(x)
( 4 [(5x-20)/4] - 20 ) / 5 Note that the expression in  is g(x)
( [5x-20] - 20 ) / 5
You can also do this with a graphing calculator.
You can also use the graphing calculator software Desmos (runs on computers, notepads, iPads, ...
I set this problem up for you to clearly indicate that these are inverses
Selectively turn the visibility of expressions 3, 4, 5 to show that the expressions 3, 4, 5 are equivalent and equal to Identity.