\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Solve \(\displaystyle \frac{4}{x - 5}=\frac{8}{x - 10}\).
The LCD is \(\displaystyle \left(x - 10\right) \left(x - 5\right)\). Multiplying by the LCD to clear the fractions gives \(\displaystyle 4 x - 40 = 8 x - 40\). Isloating \(\displaystyle x\) gives \(\displaystyle x = 0\).
\begin{question}Solve $\frac{4}{x - 5}=\frac{8}{x - 10}$.
\soln{9cm}{The LCD is $\left(x - 10\right) \left(x - 5\right)$. Multiplying by the LCD to clear the fractions gives $4 x - 40 = 8 x - 40$. Isloating $x$ gives $x = 0$. }
\end{question}
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}
\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}
\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}
\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue
\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{4}{x - 5}=\frac{8}{x - 10} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B4%7D%7Bx%20-%205%7D%3D%5Cfrac%7B8%7D%7Bx%20-%2010%7D%20" alt="LaTeX: \displaystyle \frac{4}{x - 5}=\frac{8}{x - 10} " data-equation-content=" \displaystyle \frac{4}{x - 5}=\frac{8}{x - 10} " /> .</p> </p><p> <p>The LCD is <img class="equation_image" title=" \displaystyle \left(x - 10\right) \left(x - 5\right) " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%28x%20-%2010%5Cright%29%20%5Cleft%28x%20-%205%5Cright%29%20" alt="LaTeX: \displaystyle \left(x - 10\right) \left(x - 5\right) " data-equation-content=" \displaystyle \left(x - 10\right) \left(x - 5\right) " /> . Multiplying by the LCD to clear the fractions gives <img class="equation_image" title=" \displaystyle 4 x - 40 = 8 x - 40 " src="/equation_images/%20%5Cdisplaystyle%204%20x%20-%2040%20%3D%208%20x%20-%2040%20" alt="LaTeX: \displaystyle 4 x - 40 = 8 x - 40 " data-equation-content=" \displaystyle 4 x - 40 = 8 x - 40 " /> . 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 = 0 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%200%20" alt="LaTeX: \displaystyle x = 0 " data-equation-content=" \displaystyle x = 0 " /> . </p> </p>