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Questions: Algebra BusinessCalculus
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Solve the inequality \(\displaystyle -3 \leq 7 x - 8 < 1\). Write the solution in interval notation.
Since this is a three part inequality we must do the same thing to all three parts.Adding 8 to all three parts gives \(\displaystyle -11 \leq 7 x - 8 < -7 \). Dividing off the coefficient of \(\displaystyle x\) gives \(\displaystyle - \frac{11}{7} \leq x < -1\)The solution is \(\displaystyle \big[- \frac{11}{7},-1\big)\)
\begin{question}Solve the inequality $-3 \leq 7 x - 8 < 1$. 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 8 to all three parts gives $-11 \leq 7 x - 8 < -7 $. Dividing off the coefficient of $x$ gives $- \frac{11}{7} \leq x < -1$The solution is $\big[- \frac{11}{7},-1\big)$}
\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 7 x - 8 < 1 " src="/equation_images/%20%5Cdisplaystyle%20-3%20%5Cleq%207%20x%20-%208%20%3C%201%20" alt="LaTeX: \displaystyle -3 \leq 7 x - 8 < 1 " data-equation-content=" \displaystyle -3 \leq 7 x - 8 < 1 " /> . 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 8 to all three parts gives <img class="equation_image" title=" \displaystyle -11 \leq 7 x - 8 < -7 " src="/equation_images/%20%5Cdisplaystyle%20-11%20%5Cleq%207%20x%20-%208%20%3C%20-7%20%20" alt="LaTeX: \displaystyle -11 \leq 7 x - 8 < -7 " data-equation-content=" \displaystyle -11 \leq 7 x - 8 < -7 " /> . 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{11}{7} \leq x < -1 " src="/equation_images/%20%5Cdisplaystyle%20-%20%5Cfrac%7B11%7D%7B7%7D%20%5Cleq%20x%20%3C%20-1%20" alt="LaTeX: \displaystyle - \frac{11}{7} \leq x < -1 " data-equation-content=" \displaystyle - \frac{11}{7} \leq x < -1 " /> The solution is <img class="equation_image" title=" \displaystyle \big[- \frac{11}{7},-1\big) " src="/equation_images/%20%5Cdisplaystyle%20%5Cbig%5B-%20%5Cfrac%7B11%7D%7B7%7D%2C-1%5Cbig%29%20" alt="LaTeX: \displaystyle \big[- \frac{11}{7},-1\big) " data-equation-content=" \displaystyle \big[- \frac{11}{7},-1\big) " /> </p> </p>