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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle | - 2 x - 4 | \leq 10\)
The inequality is an "and" type compound inequality. Setting up the three part inequality gives \(\displaystyle -10 \leq - 2 x - 4 \leq 10\). Doing the same thing to all three parts gives \(\displaystyle -6 \leq - 2 x \leq 14\). Isolating \(\displaystyle x\) gives \(\displaystyle 3 \geq x \geq -7\).
\begin{question}Solve $| - 2 x - 4 | \leq 10$
\soln{9cm}{The inequality is an "and" type compound inequality. Setting up the three part inequality gives $ -10 \leq - 2 x - 4 \leq 10$. Doing the same thing to all three parts gives $ -6 \leq - 2 x \leq 14$. Isolating $x$ gives $ 3 \geq x \geq -7$. }
\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 - 4 | \leq 10 " src="/equation_images/%20%5Cdisplaystyle%20%7C%20-%202%20x%20-%204%20%7C%20%5Cleq%2010%20" alt="LaTeX: \displaystyle | - 2 x - 4 | \leq 10 " data-equation-content=" \displaystyle | - 2 x - 4 | \leq 10 " /> </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 -10 \leq - 2 x - 4 \leq 10 " src="/equation_images/%20%5Cdisplaystyle%20%20-10%20%5Cleq%20-%202%20x%20-%204%20%5Cleq%2010%20" alt="LaTeX: \displaystyle -10 \leq - 2 x - 4 \leq 10 " data-equation-content=" \displaystyle -10 \leq - 2 x - 4 \leq 10 " /> . Doing the same thing to all three parts gives <img class="equation_image" title=" \displaystyle -6 \leq - 2 x \leq 14 " src="/equation_images/%20%5Cdisplaystyle%20%20-6%20%5Cleq%20-%202%20x%20%5Cleq%2014%20" alt="LaTeX: \displaystyle -6 \leq - 2 x \leq 14 " data-equation-content=" \displaystyle -6 \leq - 2 x \leq 14 " /> . 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 3 \geq x \geq -7 " src="/equation_images/%20%5Cdisplaystyle%20%203%20%5Cgeq%20x%20%5Cgeq%20-7%20" alt="LaTeX: \displaystyle 3 \geq x \geq -7 " data-equation-content=" \displaystyle 3 \geq x \geq -7 " /> . </p> </p>