QUESTION IMAGE
Question
never true
kiandra looked at this equation and, without writing anything, said it must have no solution.
what might she have noticed to lead her to this conclusion?
no solution (true for no values)
\\(\frac{1}{2} + x = \frac{1}{3} + x\\)
Kiandra noticed that the variable $x$ appears on both sides of the equation, and when removed, the remaining constants $\frac{1}{2}$ and $\frac{1}{3}$ are not equal. A valid equation requires the non-variable parts to match after eliminating identical variable terms, which fails here.
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She noticed that the equation has the same variable term ($x$) on both sides, while the constant terms $\frac{1}{2}$ and $\frac{1}{3}$ are not equal, so the equation can never be true for any value of $x$.