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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle \frac{7}{x - 5}=\frac{4}{x - 9}\).
The LCD is \(\displaystyle \left(x - 9\right) \left(x - 5\right)\). Multiplying by the LCD to clear the fractions gives \(\displaystyle 7 x - 63 = 4 x - 20\). Isloating \(\displaystyle x\) gives \(\displaystyle x = \frac{43}{3}\).
\begin{question}Solve $\frac{7}{x - 5}=\frac{4}{x - 9}$.
\soln{9cm}{The LCD is $\left(x - 9\right) \left(x - 5\right)$. Multiplying by the LCD to clear the fractions gives $7 x - 63 = 4 x - 20$. Isloating $x$ gives $x = \frac{43}{3}$. }
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Solve <img class="equation_image" title=" \displaystyle \frac{7}{x - 5}=\frac{4}{x - 9} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B7%7D%7Bx%20-%205%7D%3D%5Cfrac%7B4%7D%7Bx%20-%209%7D%20" alt="LaTeX: \displaystyle \frac{7}{x - 5}=\frac{4}{x - 9} " data-equation-content=" \displaystyle \frac{7}{x - 5}=\frac{4}{x - 9} " /> .</p> </p><p> <p>The LCD is <img class="equation_image" title=" \displaystyle \left(x - 9\right) \left(x - 5\right) " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%28x%20-%209%5Cright%29%20%5Cleft%28x%20-%205%5Cright%29%20" alt="LaTeX: \displaystyle \left(x - 9\right) \left(x - 5\right) " data-equation-content=" \displaystyle \left(x - 9\right) \left(x - 5\right) " /> . Multiplying by the LCD to clear the fractions gives <img class="equation_image" title=" \displaystyle 7 x - 63 = 4 x - 20 " src="/equation_images/%20%5Cdisplaystyle%207%20x%20-%2063%20%3D%204%20x%20-%2020%20" alt="LaTeX: \displaystyle 7 x - 63 = 4 x - 20 " data-equation-content=" \displaystyle 7 x - 63 = 4 x - 20 " /> . Isloating <img class="equation_image" title=" \displaystyle x " src="/equation_images/%20%5Cdisplaystyle%20x%20" alt="LaTeX: \displaystyle x " data-equation-content=" \displaystyle x " /> gives <img class="equation_image" title=" \displaystyle x = \frac{43}{3} " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20%5Cfrac%7B43%7D%7B3%7D%20" alt="LaTeX: \displaystyle x = \frac{43}{3} " data-equation-content=" \displaystyle x = \frac{43}{3} " /> . </p> </p>