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Questions: Algebra BusinessCalculus
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Solve the inequality \(\displaystyle 9 \leq 4 x + 5 < 16\). Write the solution in interval notation.
Since this is a three part inequality we must do the same thing to all three parts.Subtracting 5 from all three parts gives \(\displaystyle 4 \leq 4 x + 5 < 11 \). Dividing off the coefficient of \(\displaystyle x\) gives \(\displaystyle 1 \leq x < \frac{11}{4}\)The solution is \(\displaystyle \big[1,\frac{11}{4}\big)\)
\begin{question}Solve the inequality $9 \leq 4 x + 5 < 16$. 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.Subtracting 5 from all three parts gives $4 \leq 4 x + 5 < 11 $. Dividing off the coefficient of $x$ gives $1 \leq x < \frac{11}{4}$The solution is $\big[1,\frac{11}{4}\big)$}
\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 + 5 < 16 " src="/equation_images/%20%5Cdisplaystyle%209%20%5Cleq%204%20x%20%2B%205%20%3C%2016%20" alt="LaTeX: \displaystyle 9 \leq 4 x + 5 < 16 " data-equation-content=" \displaystyle 9 \leq 4 x + 5 < 16 " /> . 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.Subtracting 5 from all three parts gives <img class="equation_image" title=" \displaystyle 4 \leq 4 x + 5 < 11 " src="/equation_images/%20%5Cdisplaystyle%204%20%5Cleq%204%20x%20%2B%205%20%3C%2011%20%20" alt="LaTeX: \displaystyle 4 \leq 4 x + 5 < 11 " data-equation-content=" \displaystyle 4 \leq 4 x + 5 < 11 " /> . 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 1 \leq x < \frac{11}{4} " src="/equation_images/%20%5Cdisplaystyle%201%20%5Cleq%20x%20%3C%20%5Cfrac%7B11%7D%7B4%7D%20" alt="LaTeX: \displaystyle 1 \leq x < \frac{11}{4} " data-equation-content=" \displaystyle 1 \leq x < \frac{11}{4} " /> The solution is <img class="equation_image" title=" \displaystyle \big[1,\frac{11}{4}\big) " src="/equation_images/%20%5Cdisplaystyle%20%5Cbig%5B1%2C%5Cfrac%7B11%7D%7B4%7D%5Cbig%29%20" alt="LaTeX: \displaystyle \big[1,\frac{11}{4}\big) " data-equation-content=" \displaystyle \big[1,\frac{11}{4}\big) " /> </p> </p>