Consider the puzzle:
"I have In mind a (secret) number. When I subtract 2/5 from this number I get 7. What is the number?"
To solve such puzzles we go backwards. We got 7 after we subtracted 2/5, so if we add 2/5 to 7, we get the secret number back.
Solving an equation is solving a puzzle about a secret number, which we call "x" instead of saying "something", all the time.
going backwards, means adding, if we subtracted, or dividing, if we multiplied.
So, to solve [tex]x- \frac{2}{5}=7 [/tex], we just need to add 2/5 back to x:
[tex]x- \frac{2}{5}=7[/tex]
[tex]x- \frac{2}{5}+\frac{2}{5}=7+\frac{2}{5}[/tex]
[tex]x=7+\frac{2}{5}[/tex]
to add 7 and 2/5, multiply 7 by 5/5
7+2/5=7.(5/5)+2/5=35/5+2/5=37/5
Thus x= 37/5
