Final answer:
The statement is false as not all equations with a variable on one side and a number on the other have only one solution, especially in the case of quadratic equations which typically have two solutions.
Step-by-step explanation:
If an equation has a variable on one side and a number on the other side, it suggests there is one solution for the variable that makes the equation true. For example, if we have an equation like g = -6, solving for g simply gives us one value, which is -6. This is a typical scenario for linear equations, which often have a single solution when they are in the standard form ax + b = 0, and can be rearranged to isolate the variable x.
However, the student's statement might be false in scenarios involving non-linear equations like quadratic equations, which can have two solutions. For example, the quadratic equation x² + bx + c = 0 can be solved using the quadratic formula, which will generally yield two solutions for x due to the square term x².
Therefore, the answer to the statement is B) False, because not all equations with a variable on one side and a number on the other necessarily have only one solution.