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Questions: Algebra BusinessCalculus
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Solve the inequality \(\displaystyle -3 \leq - 6 x - 6 < -2\). 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 \(\displaystyle -9 \leq - 6 x - 6 < -8 \). Dividing off the coefficient of \(\displaystyle x\) gives and reversing all of the inequalies \(\displaystyle \frac{3}{2} \geq x > \frac{4}{3}\)The solution is \(\displaystyle \big(\frac{4}{3},\frac{3}{2}\big]\)
\begin{question}Solve the inequality $-3 \leq - 6 x - 6 < -2$. 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 $-9 \leq - 6 x - 6 < -8 $. Dividing off the coefficient of $x$ gives and reversing all of the inequalies $\frac{3}{2} \geq x > \frac{4}{3}$The solution is $\big(\frac{4}{3},\frac{3}{2}\big]$}
\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 -3 \leq - 6 x - 6 < -2 " src="/equation_images/%20%5Cdisplaystyle%20-3%20%5Cleq%20-%206%20x%20-%206%20%3C%20-2%20" alt="LaTeX: \displaystyle -3 \leq - 6 x - 6 < -2 " data-equation-content=" \displaystyle -3 \leq - 6 x - 6 < -2 " /> . 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 -9 \leq - 6 x - 6 < -8 " src="/equation_images/%20%5Cdisplaystyle%20-9%20%5Cleq%20-%206%20x%20-%206%20%3C%20-8%20%20" alt="LaTeX: \displaystyle -9 \leq - 6 x - 6 < -8 " data-equation-content=" \displaystyle -9 \leq - 6 x - 6 < -8 " /> . 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 \frac{3}{2} \geq x > \frac{4}{3} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B3%7D%7B2%7D%20%5Cgeq%20x%20%3E%20%5Cfrac%7B4%7D%7B3%7D%20" alt="LaTeX: \displaystyle \frac{3}{2} \geq x > \frac{4}{3} " data-equation-content=" \displaystyle \frac{3}{2} \geq x > \frac{4}{3} " /> The solution is <img class="equation_image" title=" \displaystyle \big(\frac{4}{3},\frac{3}{2}\big] " src="/equation_images/%20%5Cdisplaystyle%20%5Cbig%28%5Cfrac%7B4%7D%7B3%7D%2C%5Cfrac%7B3%7D%7B2%7D%5Cbig%5D%20" alt="LaTeX: \displaystyle \big(\frac{4}{3},\frac{3}{2}\big] " data-equation-content=" \displaystyle \big(\frac{4}{3},\frac{3}{2}\big] " /> </p> </p>