Using strong mathematical induction to prove a statement

Question

So I have a question that I got stuck on, it says I have to prove that all integers greater than 17 can be written using a sum of 7's and 4's. For instance 7 + 7 + 7 + 4 + 4 = 29 or 7 + 4 + 4 + 4 = 19 .... etc. Appreciate the help. Cheers.

Answer 1

If $x$ has atleast one $7$, remove it and add two $4$'s. If $x$ has all $4$'s remove five $4$'s and add three $7$'s. (In the latter case $x \geq 20$ necessarily).

If you need to use strong induction, then we have for $x-4$ when $x \geq 22$, that $x$ satisfies the condition. Then the cases for $18,19,20,21$ are clear.