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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle | 2 x - 5 | < 23\)
The inequality is an "and" type compound inequality. Setting up the three part inequality gives \(\displaystyle -23 < 2 x - 5 < 23\). Doing the same thing to all three parts gives \(\displaystyle -18 < 2 x < 28\). Isolating \(\displaystyle x\) gives \(\displaystyle -9 < x < 14\).
\begin{question}Solve $| 2 x - 5 | < 23$
\soln{9cm}{The inequality is an "and" type compound inequality. Setting up the three part inequality gives $ -23 < 2 x - 5 < 23$. Doing the same thing to all three parts gives $ -18 < 2 x < 28$. Isolating $x$ gives $ -9 < x < 14$. }
\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 | 2 x - 5 | < 23 " src="/equation_images/%20%5Cdisplaystyle%20%7C%202%20x%20-%205%20%7C%20%3C%2023%20" alt="LaTeX: \displaystyle | 2 x - 5 | < 23 " data-equation-content=" \displaystyle | 2 x - 5 | < 23 " /> </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 -23 < 2 x - 5 < 23 " src="/equation_images/%20%5Cdisplaystyle%20%20-23%20%3C%202%20x%20-%205%20%3C%2023%20" alt="LaTeX: \displaystyle -23 < 2 x - 5 < 23 " data-equation-content=" \displaystyle -23 < 2 x - 5 < 23 " /> . Doing the same thing to all three parts gives <img class="equation_image" title=" \displaystyle -18 < 2 x < 28 " src="/equation_images/%20%5Cdisplaystyle%20%20-18%20%3C%202%20x%20%3C%2028%20" alt="LaTeX: \displaystyle -18 < 2 x < 28 " data-equation-content=" \displaystyle -18 < 2 x < 28 " /> . 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 -9 < x < 14 " src="/equation_images/%20%5Cdisplaystyle%20%20-9%20%3C%20x%20%3C%2014%20" alt="LaTeX: \displaystyle -9 < x < 14 " data-equation-content=" \displaystyle -9 < x < 14 " /> . </p> </p>