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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle | 3 x - 4 | < 11\)
The inequality is an "and" type compound inequality. Setting up the three part inequality gives \(\displaystyle -11 < 3 x - 4 < 11\). Doing the same thing to all three parts gives \(\displaystyle -7 < 3 x < 15\). Isolating \(\displaystyle x\) gives \(\displaystyle - \frac{7}{3} < x < 5\).
\begin{question}Solve $| 3 x - 4 | < 11$
\soln{9cm}{The inequality is an "and" type compound inequality. Setting up the three part inequality gives $ -11 < 3 x - 4 < 11$. Doing the same thing to all three parts gives $ -7 < 3 x < 15$. Isolating $x$ gives $ - \frac{7}{3} < x < 5$. }
\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 | 3 x - 4 | < 11 " src="/equation_images/%20%5Cdisplaystyle%20%7C%203%20x%20-%204%20%7C%20%3C%2011%20" alt="LaTeX: \displaystyle | 3 x - 4 | < 11 " data-equation-content=" \displaystyle | 3 x - 4 | < 11 " /> </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 -11 < 3 x - 4 < 11 " src="/equation_images/%20%5Cdisplaystyle%20%20-11%20%3C%203%20x%20-%204%20%3C%2011%20" alt="LaTeX: \displaystyle -11 < 3 x - 4 < 11 " data-equation-content=" \displaystyle -11 < 3 x - 4 < 11 " /> . Doing the same thing to all three parts gives <img class="equation_image" title=" \displaystyle -7 < 3 x < 15 " src="/equation_images/%20%5Cdisplaystyle%20%20-7%20%3C%203%20x%20%3C%2015%20" alt="LaTeX: \displaystyle -7 < 3 x < 15 " data-equation-content=" \displaystyle -7 < 3 x < 15 " /> . 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{7}{3} < x < 5 " src="/equation_images/%20%5Cdisplaystyle%20%20-%20%5Cfrac%7B7%7D%7B3%7D%20%3C%20x%20%3C%205%20" alt="LaTeX: \displaystyle - \frac{7}{3} < x < 5 " data-equation-content=" \displaystyle - \frac{7}{3} < x < 5 " /> . </p> </p>