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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle | 10 x + 2 | \leq 2\)
The inequality is an "and" type compound inequality. Setting up the three part inequality gives \(\displaystyle -2 \leq 10 x + 2 \leq 2\). Doing the same thing to all three parts gives \(\displaystyle -4 \leq 10 x \leq 0\). Isolating \(\displaystyle x\) gives \(\displaystyle - \frac{2}{5} \leq x \leq 0\).
\begin{question}Solve $| 10 x + 2 | \leq 2$
\soln{9cm}{The inequality is an "and" type compound inequality. Setting up the three part inequality gives $ -2 \leq 10 x + 2 \leq 2$. Doing the same thing to all three parts gives $ -4 \leq 10 x \leq 0$. Isolating $x$ gives $ - \frac{2}{5} \leq x \leq 0$. }
\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 | \leq 2 " src="/equation_images/%20%5Cdisplaystyle%20%7C%2010%20x%20%2B%202%20%7C%20%5Cleq%202%20" alt="LaTeX: \displaystyle | 10 x + 2 | \leq 2 " data-equation-content=" \displaystyle | 10 x + 2 | \leq 2 " /> </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 -2 \leq 10 x + 2 \leq 2 " src="/equation_images/%20%5Cdisplaystyle%20%20-2%20%5Cleq%2010%20x%20%2B%202%20%5Cleq%202%20" alt="LaTeX: \displaystyle -2 \leq 10 x + 2 \leq 2 " data-equation-content=" \displaystyle -2 \leq 10 x + 2 \leq 2 " /> . Doing the same thing to all three parts gives <img class="equation_image" title=" \displaystyle -4 \leq 10 x \leq 0 " src="/equation_images/%20%5Cdisplaystyle%20%20-4%20%5Cleq%2010%20x%20%5Cleq%200%20" alt="LaTeX: \displaystyle -4 \leq 10 x \leq 0 " data-equation-content=" \displaystyle -4 \leq 10 x \leq 0 " /> . 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{2}{5} \leq x \leq 0 " src="/equation_images/%20%5Cdisplaystyle%20%20-%20%5Cfrac%7B2%7D%7B5%7D%20%5Cleq%20x%20%5Cleq%200%20" alt="LaTeX: \displaystyle - \frac{2}{5} \leq x \leq 0 " data-equation-content=" \displaystyle - \frac{2}{5} \leq x \leq 0 " /> . </p> </p>