Pregunta
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Complete the process of solving the equation. Fill in the missing term and select the missing description. Simplify any fractions. \[ \begin{array}{l} \frac{9}{3}+18=11 \\ \frac{9}{3}=-7 \\ q=\square \\ \text { Multiply both sides by } 3\end{array} \]

Ask by Pierce Nunez. in the United States
Dec 03,2024

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The missing term for \(q\) is \(-7\). The missing description is "Subtract 18 from both sides."

Solución

Let's solve the equation step by step. 1. Start with the original equation: \[ \frac{9}{3} + 18 = 11 \] 2. Simplify \(\frac{9}{3}\): \[ \frac{9}{3} = 3 \] So the equation becomes: \[ 3 + 18 = 11 \] 3. Now, simplify the left side: \[ 21 = 11 \] This is not true, so we need to check the next part of the process. 4. The next line states: \[ \frac{9}{3} = -7 \] This is incorrect based on our previous simplification. 5. Let's assume we are trying to solve for \(q\) in a different context. If we had an equation like: \[ q + 18 = 11 \] We would isolate \(q\) by subtracting 18 from both sides: \[ q = 11 - 18 \] Simplifying gives: \[ q = -7 \] 6. Now we can fill in the missing term and description: - The missing term for \(q\) is \(-7\). - The missing description is "Subtract 18 from both sides." So the completed process is: \[ \begin{array}{l} \frac{9}{3} + 18 = 11 \\ \frac{9}{3} = -7 \\ q = -7 \\ \text{Subtract 18 from both sides.} \end{array} \]

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Extra Insights

First, let's simplify the fraction \(\frac{9}{3}\), which equals \(3\). Now, substituting this back into the equation, we have \(3 + 18 = 11\). Clearly, this is not correct, so let’s find the correct equation to go along with it. With the equation \(3 + 18 = 11\), we can actually reframe that to look at the missed step in solving the equation. Instead of adding \(18\), we realize we should write \(18 - 18\) instead, which leads to \(3 = -7\) being the incorrect term. So, correcting our steps: 1. \(q = -7\) 2. The correct operation should be to subtract correctly from both sides. To fill in the missing term, we can see \(q = -7\), which means we have effectively solved for \(q\) incorrectly, yet our term indicates that we should multiply by \(3\)—which simply shifts the focus to a separate mathematical transformation that doesn't apply directly. Keep practicing, and feel free to adjust numbers for complementary practice!

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