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Questions: Algebra BusinessCalculus
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Solve the inequality \(\displaystyle 1 \leq 3 x - 7 < 10\). Write the solution in interval notation.
Since this is a three part inequality we must do the same thing to all three parts.Adding 7 to all three parts gives \(\displaystyle -6 \leq 3 x - 7 < 3 \). Dividing off the coefficient of \(\displaystyle x\) gives \(\displaystyle -2 \leq x < 1\)The solution is \(\displaystyle \big[-2,1\big)\)
\begin{question}Solve the inequality $1 \leq 3 x - 7 < 10$. 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 7 to all three parts gives $-6 \leq 3 x - 7 < 3 $. Dividing off the coefficient of $x$ gives $-2 \leq x < 1$The solution is $\big[-2,1\big)$}
\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 1 \leq 3 x - 7 < 10 " src="/equation_images/%20%5Cdisplaystyle%201%20%5Cleq%203%20x%20-%207%20%3C%2010%20" alt="LaTeX: \displaystyle 1 \leq 3 x - 7 < 10 " data-equation-content=" \displaystyle 1 \leq 3 x - 7 < 10 " /> . 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 7 to all three parts gives <img class="equation_image" title=" \displaystyle -6 \leq 3 x - 7 < 3 " src="/equation_images/%20%5Cdisplaystyle%20-6%20%5Cleq%203%20x%20-%207%20%3C%203%20%20" alt="LaTeX: \displaystyle -6 \leq 3 x - 7 < 3 " data-equation-content=" \displaystyle -6 \leq 3 x - 7 < 3 " /> . 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 -2 \leq x < 1 " src="/equation_images/%20%5Cdisplaystyle%20-2%20%5Cleq%20x%20%3C%201%20" alt="LaTeX: \displaystyle -2 \leq x < 1 " data-equation-content=" \displaystyle -2 \leq x < 1 " /> The solution is <img class="equation_image" title=" \displaystyle \big[-2,1\big) " src="/equation_images/%20%5Cdisplaystyle%20%5Cbig%5B-2%2C1%5Cbig%29%20" alt="LaTeX: \displaystyle \big[-2,1\big) " data-equation-content=" \displaystyle \big[-2,1\big) " /> </p> </p>