Question

Consider the equation you circled as having infinite solutions. What does it mean if an equation has infinite solutions. (This is a 8th grade math question about solving linear equations)
Answer in a 8th graders words

Answer 1

"Infinite solutions" means every possible number you try for the variable makes the equation true. In other words, there isn't just one answer — there are infinitely many answers (every number works).

How to see it:
- Simplify both sides first.
- If the variables cancel out and you end up with a true statement like 0 = 0 or 5 = 5, then the equation is true for all x → infinite solutions.
- If the variables cancel and you get a false statement like 3 = 7, then there are no solutions.
- If you can solve and get a single number like x = 4, then there is one solution.

Examples:
- x + 2 = x + 2 → variables cancel and you get 2 = 2, so every number for x works (infinite solutions).
- 2x + 3 = 2x + 1 → variables cancel and you get 3 = 1, which is false, so no solution.
- 2x + 1 = 7 → subtract 1 and divide by 2 to get x = 3, one solution.