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Questions: Algebra BusinessCalculus
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Solve the inequality \(\displaystyle -9 \leq 8 x - 6 < -3\). Write the solution in interval notation.
Since this is a three part inequality we must do the same thing to all three parts.Adding 6 to all three parts gives \(\displaystyle -15 \leq 8 x - 6 < -9 \). Dividing off the coefficient of \(\displaystyle x\) gives \(\displaystyle - \frac{15}{8} \leq x < - \frac{9}{8}\)The solution is \(\displaystyle \big[- \frac{15}{8},- \frac{9}{8}\big)\)
\begin{question}Solve the inequality $-9 \leq 8 x - 6 < -3$. Write the solution in interval notation. \newline
\soln{9cm}{Since this is a three part inequality we must do the same thing to all three parts.Adding 6 to all three parts gives $-15 \leq 8 x - 6 < -9 $. Dividing off the coefficient of $x$ gives $- \frac{15}{8} \leq x < - \frac{9}{8}$The solution is $\big[- \frac{15}{8},- \frac{9}{8}\big)$}
\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 the inequality <img class="equation_image" title=" \displaystyle -9 \leq 8 x - 6 < -3 " src="/equation_images/%20%5Cdisplaystyle%20-9%20%5Cleq%208%20x%20-%206%20%3C%20-3%20" alt="LaTeX: \displaystyle -9 \leq 8 x - 6 < -3 " data-equation-content=" \displaystyle -9 \leq 8 x - 6 < -3 " /> . Write the solution in interval notation. <br> </p> </p>
<p> <p>Since this is a three part inequality we must do the same thing to all three parts.Adding 6 to all three parts gives <img class="equation_image" title=" \displaystyle -15 \leq 8 x - 6 < -9 " src="/equation_images/%20%5Cdisplaystyle%20-15%20%5Cleq%208%20x%20-%206%20%3C%20-9%20%20" alt="LaTeX: \displaystyle -15 \leq 8 x - 6 < -9 " data-equation-content=" \displaystyle -15 \leq 8 x - 6 < -9 " /> . Dividing off the coefficient of <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{15}{8} \leq x < - \frac{9}{8} " src="/equation_images/%20%5Cdisplaystyle%20-%20%5Cfrac%7B15%7D%7B8%7D%20%5Cleq%20x%20%3C%20-%20%5Cfrac%7B9%7D%7B8%7D%20" alt="LaTeX: \displaystyle - \frac{15}{8} \leq x < - \frac{9}{8} " data-equation-content=" \displaystyle - \frac{15}{8} \leq x < - \frac{9}{8} " /> The solution is <img class="equation_image" title=" \displaystyle \big[- \frac{15}{8},- \frac{9}{8}\big) " src="/equation_images/%20%5Cdisplaystyle%20%5Cbig%5B-%20%5Cfrac%7B15%7D%7B8%7D%2C-%20%5Cfrac%7B9%7D%7B8%7D%5Cbig%29%20" alt="LaTeX: \displaystyle \big[- \frac{15}{8},- \frac{9}{8}\big) " data-equation-content=" \displaystyle \big[- \frac{15}{8},- \frac{9}{8}\big) " /> </p> </p>