Number of solutions, step by step
Some equations have one answer, some none at all, and some are true for every number.
The question
How many solutions?
17x + 25 = 25 + 17x
17x + 25 = 25 + 17x
17x + 25 = 25 + 17x
x is gone
25 = 25is true
infinitely many solutions
- Do not start by hunting for x. Ask a smaller question first: what is left when the x terms are collected on one side?
- Both sides have the SAME number of x, so taking it off both sides removes x completely. That is not a mistake — it is the answer arriving early.
- What is left is 25 = 25, which is true whatever x is. So every number works — infinitely many solutions.
How it works.
- 01
Do not start by hunting for x. Ask a smaller question first: what is left when the x terms are collected on one side?
- 02
Both sides have the SAME number of x, so taking it off both sides removes x completely. That is not a mistake — it is the answer arriving early.
- 03
What is left is 25 = 25, which is true whatever x is. So every number works — infinitely many solutions.