Context: The equation $35x - 25 = 5(7x - 5)$ is given, and the task is to count how many solutions it has.

Answer: C) Infinitely many

Why? Distributing the right side gives $5(7x - 5) = 35x - 25$, so the equation reads $35x - 25 = 35x - 25$. The two sides are the same expression, so every value of $x$ satisfies it.

Traps:

• A) Exactly one solution requires the $x$ terms to differ, leaving a nonzero coefficient once they are collected, as in $35x - 25 = 7x - 5$.
• B) A linear equation can never have exactly two solutions; collecting the $x$ terms leaves one solution, none, or all values.
• D) Zero solutions requires matching $x$ terms with different constants, as in $35x - 25 = 35x - 20$, which collapses to a false statement.