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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle | x + 1 | > 17\)
The inequality is an "or" type compound inequality. This gives the two inequalities \(\displaystyle x + 1 < -17\) or \(\displaystyle x + 1 > 17\). Solving gives \(\displaystyle x < -18\) or \(\displaystyle x > 16\). Isolating \(\displaystyle x\) gives \(\displaystyle x < -18\) or \(\displaystyle x > 16\).
\begin{question}Solve $| x + 1 | > 17$
\soln{9cm}{The inequality is an "or" type compound inequality. This gives the two inequalities $x + 1 < -17$ or $x + 1 > 17$. Solving gives $x < -18$ or $x > 16$. Isolating $x$ gives $x < -18$ or $x > 16$. }
\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 | x + 1 | > 17 " src="/equation_images/%20%5Cdisplaystyle%20%7C%20x%20%2B%201%20%7C%20%3E%2017%20" alt="LaTeX: \displaystyle | x + 1 | > 17 " data-equation-content=" \displaystyle | x + 1 | > 17 " /> </p> </p>
<p> <p>The inequality is an "or" type compound inequality. This gives the two inequalities <img class="equation_image" title=" \displaystyle x + 1 < -17 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%201%20%3C%20-17%20" alt="LaTeX: \displaystyle x + 1 < -17 " data-equation-content=" \displaystyle x + 1 < -17 " /> or <img class="equation_image" title=" \displaystyle x + 1 > 17 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%201%20%3E%2017%20" alt="LaTeX: \displaystyle x + 1 > 17 " data-equation-content=" \displaystyle x + 1 > 17 " /> . Solving gives <img class="equation_image" title=" \displaystyle x < -18 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3C%20-18%20" alt="LaTeX: \displaystyle x < -18 " data-equation-content=" \displaystyle x < -18 " /> or <img class="equation_image" title=" \displaystyle x > 16 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3E%2016%20" alt="LaTeX: \displaystyle x > 16 " data-equation-content=" \displaystyle x > 16 " /> . 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 < -18 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3C%20-18%20" alt="LaTeX: \displaystyle x < -18 " data-equation-content=" \displaystyle x < -18 " /> or <img class="equation_image" title=" \displaystyle x > 16 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3E%2016%20" alt="LaTeX: \displaystyle x > 16 " data-equation-content=" \displaystyle x > 16 " /> . </p> </p>