You will want to pay attention to this section. The reason for this is that you are accustomed to \textit{always expanding brackets}, but now we sometimes do not!


\begin{demobox}
    \subsection*{Solve:}
    \begin{enumerate}[a)]
        \item \[3(x+2)=21\]
        \subsection*{Solution}
            \[
            \begin{aligned}
            x+2 & =7 \quad \text { (Divide both sides by 3.) } \\
            x & =5
            \end{aligned}
            \]

        \item \[2(3-x)=12\]
        \subsection*{Solution}
            \(3-x=6 \quad\) (Divide both sides by 2.)

            \(-x=3\)

            \[
            x=-3
            \]
    \end{enumerate}
\end{demobox}

\begin{examplebox}
    \subsection{Examples:}
    \begin{questions}
        \questionpoints[1] Solve \(3(x+5)=31\)
        \begin{solutionordottedlines}[1in]
            \begin{multicols}{2}
            \section*{Method 1}
            \(3(x+5)=31\)

            \(3 x+15=31\)

            \(3 x=16\)

            \(x=\frac{16}{3}\)

            \(x=5 \frac{1}{3}\)

            \section*{Method 2}
            \[
            \begin{array}{r}
            3(x+5)=31 \\
            x+5=\frac{31}{3} \\
            x=\frac{16}{3}
            \end{array}
            \]
            \end{multicols}
        \end{solutionordottedlines}
        \questionpoints[3] Solve:
        \begin{parts}
            \part \(2(x+1)+4(x+3)=26\)
            \begin{solutionordottedlines}[2cm]
                \(2(x+1)+4(x+3)=26\)

                \(2 x+2+4 x+12=26\)

                \(6 x+14=26\)

                (Expand the brackets.)

                \(6 x=12\)

                \(x=2\)
            \end{solutionordottedlines}
            \part \(3(a+5)=2(a+6)\)
            \begin{solutionordottedlines}[2cm]
                \(3(a+5)=2(a+6)\)

                \(3 a+15=2 a+12\)

                \(a+15=12\)

                \(a=-3\)

                (Subtract \(2 a\) from both sides.)
            \end{solutionordottedlines}
            \part \(3(y-3)-2(y-4)=4\)
            \begin{solutionordottedlines}[2cm]
                \(3(y-3)-2(y-4)=4\)

                \(3 y-9-2 y+8=4\)

                \(y-1=4\)

                (Expand both sets of brackets,

                being careful with the signs.)

                \(y=5\)
            \end{solutionordottedlines}
        \end{parts}
    \end{questions}
\end{examplebox}


\begin{exercisebox}
    \subsection{Exercises:}
    \begin{questions}
        \questionpoints[12] Solve for \(x\).
        \begin{parts}\begin{multicols}{2}
            \part \(2(x+3)=8\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(5(x+1)=10\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(-3(2 x-6)=12\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(2(x+3)=15\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(4(7-x)=7\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(5(x-3)=\frac{2}{3}\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(2(a+1)+4(a+2)=22\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(5(c+2)-2(c+1)=17\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(2(x+3)-3(x-4)=20\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(5(a+3)=3(2 a+1)\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(-2(x+4)+3(x-2)=16\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{1}{2}(2 x+5)+6(x-2)=4 \frac{1}{2}\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
    \end{questions}
\end{exercisebox}
