algebra problem help

[cookderosa]

Can someone please take pity on my lack of math skill and help me understand something? I keep missing the same type of question, getting stuck at the same place. Perhaps I am not approaching the problem correctly, but for the life of me I can't get to the solution. Here are just 2 problem that can't solve, but I have missed 100% of every problem that ends up with an improper fraction as the answer to the variable.

1. 20x - 23 = 14x - 13
+13 to both sides
20x -10 = 14x
-14 from both sides
6x - 10 = x
(stuck)
the correct answer is 5/3

2. 42x + 40 = 7x
-7 both sides
35x + 40 = x
(stuck)
the correct answer is 8/7