An equation that is true for all values of x and has an infinite number of solutions simplifies to an identity or tautology, where all terms cancel out or are equal on both sides.
The student has asked which equation would be true for all values of x, implying it has an infinite number of solutions. An equation with an infinite number of solutions is typically one where both sides of the equation are identical after simplification, which means all terms involving variables and constants cancel out. An example of such an equation can be x + 5 = x + 5, where no matter what value x takes, both sides of the equation will always be equal.
Other times, an equation might initially contain a variable, but upon rearrangement or simplification, it turns into an identity (e.g., 3(x-2) = 3x - 6), which is another way an equation can have infinite solutions. When substituting equilibrium concentration terms into the solubility product expression, if you properly rearrange to solve for x and find that every term containing x cancels out, you would be left with a statement that is always true.
An equation that simplifies to an identity or a tautology is true for all values of x and therefore has an infinite number of solutions.