How many solutions?, step by step
Some equations have one answer, some have none at all, and some are true for every number.
The question
How many solutions?
2(−x + 6) = −2x + 12
2(−x + 6) = −2x + 12
2(−x + 6) = −2x + 12
2(−x + 6) = −2x + 12
x is gone
12 = 12is 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?
- The bracket has to come off before the two sides can be compared at all — multiply everything inside it by the number outside.
- 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 12 = 12, 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
The bracket has to come off before the two sides can be compared at all — multiply everything inside it by the number outside.
- 03
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.
- 04
What is left is 12 = 12, which is true whatever x is. So every number works — infinitely many solutions.