This is the punchline of today's lesson, and an important new concept for you all to grasp: \textbf{\textsc{Inequalities}}. The symbols for them are:
\begin{enumerate}\begin{multicols}{2}
    \item $>$ = \fillin[greater than][0.3\textwidth]
    \item $<$ = \fillin[less than][0.3\textwidth]
    \item $\leq$ = \fillin[less than or equal to][0.3\textwidth]
    \item $\geq$ = \fillin[greater than or equal to][0.3\textwidth]
\end{multicols}\end{enumerate}

\begin{examplebox}
    \subsection{Examples:}
    \begin{questions}
        \Question[1] $4 \fillin[<] 6$
        \Question[1] $5 \fillin[>] 3$
        \Question[1] $2 \fillin[=] 2$
        \Question[1] $-2 \fillin[>] -10$
        \Question[1] $8 \fillin[>] -8$
    \end{questions}
    Let us now visualise these inequalities on a number line:
    \begin{questions}
        \Question[1] $x<2$:
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
        \Question[1] $x\geq-1$
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
    \end{questions}
    Here is some more practise:
    \begin{questions}
        \Question[3] Graph each set on the number line.
        \begin{parts}
            \part \(\{x: x \leq-2\}\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(\{x: x>3\}\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(\left\{x: x \geq 3 \frac{1}{2}\right\}\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
        \end{parts}
    \end{questions}
\end{examplebox}


\begin{exercisebox}
    \subsection{Exercises:}
    \begin{questions}
        \Question[3] Copy and insert \(>\) or \(<\) to make each statement true.
        \begin{parts}
            \part \(7 \fillin[>] 2\)
            \part \(-54 \fillin[>] -500\)
            \part \(21 \fillin[<] 40\)
        \end{parts}
        \Question[3] Copy and insert \(\leq\) or \(\geq\) to make each statement true.
        \begin{parts}
            \part \(-7 \fillin[\leq]-2\)
            \part \(-10 \fillin[\geq]-50\)
            \part \(12 \fillin[\leq] 26\)
        \end{parts}
        \Question[5] Use set notation to describe each interval.
        \begin{center}
        \begin{parts}
            \part \ineqLine{-4}{3}{-2}{1.5}{0}
            \begin{solutionorbox}[2cm]
                \[\{x:x>-2\}\]
            \end{solutionorbox}
            \part \ineqLine{-6}{1}{-2}{-5}{0}
            \begin{solutionorbox}[2cm]
                \[\{x:x<-2\}\]
            \end{solutionorbox}
            \part \ineqLine[1.5]{-6}{1}{-2.5}{-4.8}{1}
            \begin{solutionorbox}[2cm]
                \[\{x:x\leq -2.5\}\]
            \end{solutionorbox}
        \end{parts}
            \end{center}
    \end{questions}
\end{exercisebox}


