JUSTIFIES A STEP IN THE SOLUTION OF AN EQUATION

4n+(7+n)=52
4n+(n+7)=52
(4n+n)+7=52
5n+7=52
5n+7-7=52
5n=45
5n/5=45/9
n=9

Oh my ....

necessary steps:

4n+(7+n)=52
4n + 7 + n = 52
5n + 7 = 52
5n = 52-7
5n = 45
n = 9

Your 4th last line should have been
5n+7-7 = 52-7 , ( remember "whatever you do to one side, you must do to the other". You didn't )