The expression on the left side of an equation is shown below. \( \begin{array}{l}3 x+9=\square \\ \text { If the equation has no solution, which expression can be written in the box on the other side of the equation? } \\ -9 \\ -3 \\ 3 x \\ 3 x+9\end{array} \)
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Bonus Knowledge
To create an equation with no solution, the expression in the box must contradict the left side of the equation. For example, if the box contains \(3x\), this means that the equation would read \(3x + 9 = 3x\). Simplifying that results in \(9 = 0\), which is a contradiction and hence has no solution. If we were to place values like \(-9\) or \(-3\) in the box, we would find that those could lead to valid equations under certain conditions. So, the answer that guarantees no solution is placing \(3x\) in the box.
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