Solving using the inverse operations is to have the variable on one side of the equation, and a number on the other side.
In 5t+8=43, You have a number on one side of the equation, but you have the variable AND another number on the other side. This is what we need to remove.
When you have an equality, You have the right to subtract the same number from both sides, so in this case, to get ride of the 8 in "5t+8", you subtract 8 from each side of the equation:
5t + 8 = 43
5t + 8 - 8 = 43 - 8
5t = 35
t = 7
You can re-check your answer by replacing t by 7 in the initial equation:
5t + 8 = 43
5*7 + 8 = 35 + 8 = 43
Hope this helps! :D