\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Solve the inequality \(\displaystyle -4 \leq 3 - 8 x < 14\). Write the solution in interval notation.
Since this is a three part inequality we must do the same thing to all three parts.Subtracting 3 from all three parts gives \(\displaystyle -7 \leq 3 - 8 x < 11 \). Dividing off the coefficient of \(\displaystyle x\) gives and reversing all of the inequalies \(\displaystyle \frac{7}{8} \geq x > - \frac{11}{8}\)The solution is \(\displaystyle \big(- \frac{11}{8},\frac{7}{8}\big]\)
\begin{question}Solve the inequality $-4 \leq 3 - 8 x < 14$. 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 3 from all three parts gives $-7 \leq 3 - 8 x < 11 $. Dividing off the coefficient of $x$ gives and reversing all of the inequalies $\frac{7}{8} \geq x > - \frac{11}{8}$The solution is $\big(- \frac{11}{8},\frac{7}{8}\big]$}
\end{question}
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}
\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}
\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}
\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue
\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 -4 \leq 3 - 8 x < 14 " src="/equation_images/%20%5Cdisplaystyle%20-4%20%5Cleq%203%20-%208%20x%20%3C%2014%20" alt="LaTeX: \displaystyle -4 \leq 3 - 8 x < 14 " data-equation-content=" \displaystyle -4 \leq 3 - 8 x < 14 " /> . 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 3 from all three parts gives <img class="equation_image" title=" \displaystyle -7 \leq 3 - 8 x < 11 " src="/equation_images/%20%5Cdisplaystyle%20-7%20%5Cleq%203%20-%208%20x%20%3C%2011%20%20" alt="LaTeX: \displaystyle -7 \leq 3 - 8 x < 11 " data-equation-content=" \displaystyle -7 \leq 3 - 8 x < 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 and reversing all of the inequalies <img class="equation_image" title=" \displaystyle \frac{7}{8} \geq x > - \frac{11}{8} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B7%7D%7B8%7D%20%5Cgeq%20x%20%3E%20-%20%5Cfrac%7B11%7D%7B8%7D%20" alt="LaTeX: \displaystyle \frac{7}{8} \geq x > - \frac{11}{8} " data-equation-content=" \displaystyle \frac{7}{8} \geq x > - \frac{11}{8} " /> The solution is <img class="equation_image" title=" \displaystyle \big(- \frac{11}{8},\frac{7}{8}\big] " src="/equation_images/%20%5Cdisplaystyle%20%5Cbig%28-%20%5Cfrac%7B11%7D%7B8%7D%2C%5Cfrac%7B7%7D%7B8%7D%5Cbig%5D%20" alt="LaTeX: \displaystyle \big(- \frac{11}{8},\frac{7}{8}\big] " data-equation-content=" \displaystyle \big(- \frac{11}{8},\frac{7}{8}\big] " /> </p> </p>