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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle | 1 - 6 x | > 31\)
The inequality is an "or" type compound inequality. This gives the two inequalities \(\displaystyle 1 - 6 x < -31\) or \(\displaystyle 1 - 6 x > 31\). Solving gives \(\displaystyle - 6 x < -32\) or \(\displaystyle - 6 x > 30\). Isolating \(\displaystyle x\) gives \(\displaystyle x > \frac{16}{3}\) or \(\displaystyle x < -5\).
\begin{question}Solve $| 1 - 6 x | > 31$
\soln{9cm}{The inequality is an "or" type compound inequality. This gives the two inequalities $1 - 6 x < -31$ or $1 - 6 x > 31$. Solving gives $- 6 x < -32$ or $- 6 x > 30$. Isolating $x$ gives $x > \frac{16}{3}$ or $x < -5$. }
\end{question}
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\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Solve <img class="equation_image" title=" \displaystyle | 1 - 6 x | > 31 " src="/equation_images/%20%5Cdisplaystyle%20%7C%201%20-%206%20x%20%7C%20%3E%2031%20" alt="LaTeX: \displaystyle | 1 - 6 x | > 31 " data-equation-content=" \displaystyle | 1 - 6 x | > 31 " /> </p> </p>
<p> <p>The inequality is an "or" type compound inequality. This gives the two inequalities <img class="equation_image" title=" \displaystyle 1 - 6 x < -31 " src="/equation_images/%20%5Cdisplaystyle%201%20-%206%20x%20%3C%20-31%20" alt="LaTeX: \displaystyle 1 - 6 x < -31 " data-equation-content=" \displaystyle 1 - 6 x < -31 " /> or <img class="equation_image" title=" \displaystyle 1 - 6 x > 31 " src="/equation_images/%20%5Cdisplaystyle%201%20-%206%20x%20%3E%2031%20" alt="LaTeX: \displaystyle 1 - 6 x > 31 " data-equation-content=" \displaystyle 1 - 6 x > 31 " /> . Solving gives <img class="equation_image" title=" \displaystyle - 6 x < -32 " src="/equation_images/%20%5Cdisplaystyle%20-%206%20x%20%3C%20-32%20" alt="LaTeX: \displaystyle - 6 x < -32 " data-equation-content=" \displaystyle - 6 x < -32 " /> or <img class="equation_image" title=" \displaystyle - 6 x > 30 " src="/equation_images/%20%5Cdisplaystyle%20-%206%20x%20%3E%2030%20" alt="LaTeX: \displaystyle - 6 x > 30 " data-equation-content=" \displaystyle - 6 x > 30 " /> . 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 x > \frac{16}{3} " src="/equation_images/%20%5Cdisplaystyle%20x%20%3E%20%5Cfrac%7B16%7D%7B3%7D%20" alt="LaTeX: \displaystyle x > \frac{16}{3} " data-equation-content=" \displaystyle x > \frac{16}{3} " /> or <img class="equation_image" title=" \displaystyle x < -5 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3C%20-5%20" alt="LaTeX: \displaystyle x < -5 " data-equation-content=" \displaystyle x < -5 " /> . </p> </p>