How many solutions does this equation have? \[ 14-11 q=-13 q+10+2 q \]

First, let's simplify the equation step by step. We can start by combining like terms. The equation is: \[ 14 - 11q = -13q + 10 + 2q \] On the right side, we can combine \(-13q\) and \(2q\): \[ 14 - 11q = -11q + 10 \] Next, we see that both sides have \(-11q\), making it easy to isolate the constant terms: \[ 14 = 10 \] This is a contradiction, since \(14\) does not equal \(10\). Since we reached a false statement, it means there are no solutions to the equation. Thus, the equation has zero solutions! If you think about it, this is like finding a mythical unicorn—you set out in search of a solution only to discover there’s nothing there! Just remember, in mathematics, sometimes the journey leads us to unexpected truths.