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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle | 10 x - 2 | < 128\)
The inequality is an "and" type compound inequality. Setting up the three part inequality gives \(\displaystyle -128 < 10 x - 2 < 128\). Doing the same thing to all three parts gives \(\displaystyle -126 < 10 x < 130\). Isolating \(\displaystyle x\) gives \(\displaystyle - \frac{63}{5} < x < 13\).
\begin{question}Solve $| 10 x - 2 | < 128$
\soln{9cm}{The inequality is an "and" type compound inequality. Setting up the three part inequality gives $ -128 < 10 x - 2 < 128$. Doing the same thing to all three parts gives $ -126 < 10 x < 130$. Isolating $x$ gives $ - \frac{63}{5} < x < 13$. }
\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 | 10 x - 2 | < 128 " src="/equation_images/%20%5Cdisplaystyle%20%7C%2010%20x%20-%202%20%7C%20%3C%20128%20" alt="LaTeX: \displaystyle | 10 x - 2 | < 128 " data-equation-content=" \displaystyle | 10 x - 2 | < 128 " /> </p> </p>
<p> <p>The inequality is an "and" type compound inequality. Setting up the three part inequality gives <img class="equation_image" title=" \displaystyle -128 < 10 x - 2 < 128 " src="/equation_images/%20%5Cdisplaystyle%20%20-128%20%3C%2010%20x%20-%202%20%3C%20128%20" alt="LaTeX: \displaystyle -128 < 10 x - 2 < 128 " data-equation-content=" \displaystyle -128 < 10 x - 2 < 128 " /> . Doing the same thing to all three parts gives <img class="equation_image" title=" \displaystyle -126 < 10 x < 130 " src="/equation_images/%20%5Cdisplaystyle%20%20-126%20%3C%2010%20x%20%3C%20130%20" alt="LaTeX: \displaystyle -126 < 10 x < 130 " data-equation-content=" \displaystyle -126 < 10 x < 130 " /> . Isolating <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 - \frac{63}{5} < x < 13 " src="/equation_images/%20%5Cdisplaystyle%20%20-%20%5Cfrac%7B63%7D%7B5%7D%20%3C%20x%20%3C%2013%20" alt="LaTeX: \displaystyle - \frac{63}{5} < x < 13 " data-equation-content=" \displaystyle - \frac{63}{5} < x < 13 " /> . </p> </p>