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Questions: Algebra BusinessCalculus
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Solve the inequality \(\displaystyle 9 \leq - 4 x - 9 < 22\). Write the solution in interval notation.
Since this is a three part inequality we must do the same thing to all three parts.Adding 9 to all three parts gives \(\displaystyle 0 \leq - 4 x - 9 < 13 \). Dividing off the coefficient of \(\displaystyle x\) gives and reversing all of the inequalies \(\displaystyle 0 \geq x > - \frac{13}{4}\)The solution is \(\displaystyle \big(- \frac{13}{4},0\big]\)
\begin{question}Solve the inequality $9 \leq - 4 x - 9 < 22$. 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 9 to all three parts gives $0 \leq - 4 x - 9 < 13 $. Dividing off the coefficient of $x$ gives and reversing all of the inequalies $0 \geq x > - \frac{13}{4}$The solution is $\big(- \frac{13}{4},0\big]$}
\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 - 4 x - 9 < 22 " src="/equation_images/%20%5Cdisplaystyle%209%20%5Cleq%20-%204%20x%20-%209%20%3C%2022%20" alt="LaTeX: \displaystyle 9 \leq - 4 x - 9 < 22 " data-equation-content=" \displaystyle 9 \leq - 4 x - 9 < 22 " /> . 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 9 to all three parts gives <img class="equation_image" title=" \displaystyle 0 \leq - 4 x - 9 < 13 " src="/equation_images/%20%5Cdisplaystyle%200%20%5Cleq%20-%204%20x%20-%209%20%3C%2013%20%20" alt="LaTeX: \displaystyle 0 \leq - 4 x - 9 < 13 " data-equation-content=" \displaystyle 0 \leq - 4 x - 9 < 13 " /> . 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 and reversing all of the inequalies <img class="equation_image" title=" \displaystyle 0 \geq x > - \frac{13}{4} " src="/equation_images/%20%5Cdisplaystyle%200%20%5Cgeq%20x%20%3E%20-%20%5Cfrac%7B13%7D%7B4%7D%20" alt="LaTeX: \displaystyle 0 \geq x > - \frac{13}{4} " data-equation-content=" \displaystyle 0 \geq x > - \frac{13}{4} " /> The solution is <img class="equation_image" title=" \displaystyle \big(- \frac{13}{4},0\big] " src="/equation_images/%20%5Cdisplaystyle%20%5Cbig%28-%20%5Cfrac%7B13%7D%7B4%7D%2C0%5Cbig%5D%20" alt="LaTeX: \displaystyle \big(- \frac{13}{4},0\big] " data-equation-content=" \displaystyle \big(- \frac{13}{4},0\big] " /> </p> </p>