Question

how many solutions does this equation have?
-3 + 2m = 3 + 2m
no solution
one solution
infinitely many solutions

Explanation:

Step1: Subtract \(2m\) from both sides

To simplify the equation \(-3 + 2m = 3 + 2m\), we subtract \(2m\) from both sides. This gives us \(-3 + 2m - 2m = 3 + 2m - 2m\). Simplifying both sides, the \(2m\) terms cancel out, resulting in \(-3 = 3\).

Step2: Analyze the result

The equation \(-3 = 3\) is a false statement. In linear equations, if after simplifying we get a false statement, it means the original equation has no solution because there is no value of \(m\) that can make \(-3\) equal to \(3\).

Answer:

no solution