\subsection{Using linear equations to solve problems}
\begin{questions}
    \Question[2] Ping and Anna compete in a handicap sprint race. Anna starts the race \(10 \mathrm{~m}\) ahead of Ping. Ping runs at an average speed that is \(20 \%\) faster than Anna's average speed. The two sprinters will be level in the race after 9 seconds. Find the average speed of:
    \begin{parts}
        \part Anna
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part Ping
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
    \end{parts}
    \Question[1] Yolan buys 8 pens and receives 80 cents change from \(\$ 20.00\). How much does a pen cost, assuming each pen costs the same amount?
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
    \Question[1] If the sum of \(2 p\) and 19 is the same as the sum of \(4 p\) and 11 , find the value of \(p\).
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
    \Question[2] If the sum of half of \(q\) and 6 is equal to the sum of one-third of \(q\) and 2, find the value of \(q\).
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
    \Question[3] The length of a swimming pool is \(2 \mathrm{~m}\) more than four times its width.
    \begin{parts}
        \part If \(x\) metres represents the width of the pool, express the length of the pool in terms of \(x\).
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part If the perimeter of the pool is \(124 \mathrm{~m}\) find the length and width of the pool.
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
    \end{parts}
    \Question[3] Ms Minas earns \(\$ 3600\) more than Mr Brown, and Ms Lee earns \(\$ 2000\) less than Mr Brown.
    \begin{parts}
        \part If \(\$ x\) represents Mr Brown's salary, express the salary of:
        \begin{subparts}
            \subpart Ms Minas in terms of \(x\)
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
            \subpart Ms Lee in terms of \(x\)
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \end{subparts}
        \part If the total of the three incomes is \(\$ 151600\), find the income of each person.
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
    \end{parts}
\end{questions}

\subsection{Literal Equations}

\begin{questions}
    \Question[10] Rewrite in terms of $x$:
    \begin{parts}\begin{multicols}{2}
        \part \(-x+m=n\)
        \begin{solutionordottedlines}[2cm]
        \end{solutionordottedlines}
        \part \(c-b x=e\)
        \begin{solutionordottedlines}[2cm]
        \end{solutionordottedlines}
        \part \(m(n x+p)=n\)
        \begin{solutionordottedlines}[2cm]
        \end{solutionordottedlines}
        \part \(\frac{x+a}{b}=c\)
        \begin{solutionordottedlines}[2cm]
        \end{solutionordottedlines}
        \part \(\frac{m x}{n}=p\)
        \begin{solutionordottedlines}[2cm]
        \end{solutionordottedlines}
        \part \(\frac{a x+b}{c}=d\)
        \begin{solutionordottedlines}[2cm]
        \end{solutionordottedlines}
        \part \(\frac{x}{f}+\frac{g}{h}=k\)
        \begin{solutionordottedlines}[2cm]
        \end{solutionordottedlines}
        \part \(\frac{x}{b}-b=\frac{a}{b}\)
        \begin{solutionordottedlines}[2cm]
        \end{solutionordottedlines}
        \part \(m x+n=n x-m\)
        \begin{solutionordottedlines}[2cm]
        \end{solutionordottedlines}
        \part \(a(x-b)=c(x-d)\)
        \begin{solutionordottedlines}[2cm]
        \end{solutionordottedlines}
    \end{multicols}\end{parts}
\end{questions}

\subsection{Inequalities}

\begin{questions}
    \Question[3] Fill in the missing blanks with \(>\), \(<\) or $=$ to make each statement true.
    \begin{parts}
        \part \(3 \fillin[>] -4\)
        \part \(-6 \fillin[<] 0\)
        \part \(-2 \fillin[<] 5\)
        \part \(5 \fillin[5] -7\)
        \part \(0 \fillin[=] 0\)
        \part \(9 \fillin[=] 9\)
    \end{parts}
    \Question[3] Use set notation to describe each interval:
    \begin{parts}
        \part \ineqLine{-1}{5}{4}{0.8}{1}
        \begin{solutionorbox}[1in]
        \end{solutionorbox}
        \part \ineqLine{-1}{6}{1}{5}{1}
        \begin{solutionorbox}[1in]
        \end{solutionorbox}
        \part \ineqLine[1.5]{-4}{3}{-1.66}{1.8}{0}
        \begin{solutionorbox}[1in]
        \end{solutionorbox}
    \end{parts}
\end{questions}

\subsection{Solving linear inequalities}

\begin{questions}
    \Question[3] Solve and also sketch:
    \begin{parts}
        \part \[x-2<3\]
        \begin{solutionorbox}[1in]
        \end{solutionorbox}
        \part \[x-5>-12\]
        \begin{solutionorbox}[1in]
        \end{solutionorbox}
        \part \[\frac{x}{5} \geq 4\]
        \begin{solutionorbox}[1in]
        \end{solutionorbox}
    \end{parts}
    \Question[14] Just solve:
    \begin{parts}
        \part \[4 x-6 \leq-2\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part \[3(x+5) \geq 9\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part \[\frac{2 x}{5}+\frac{1}{4}>4\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part \[-10 x \geq 130\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part \[-\frac{x}{7} \geq 4\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part \[-\frac{x}{2} \geq-8\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part \[2-5 x \leq-8\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part \[4-\frac{2 x}{5} \geq 6\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part \[\frac{2 x-1}{3}-\frac{3 x+2}{4}>3\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part \[2.4-0.7 x \leq 12.9\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part \[2.8(x-4)>1.3(x+3.5)\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part \[-5 x+3 \geq 78\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part \[-\frac{x+2}{3} \leq 7\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \part \[\frac{x}{4}>-\frac{x+12}{5}\]
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
    \end{parts}
    \Question[2] The sum of \(4 d\) and 6 is greater than the sum of \(2 d\) and 18 . What values can \(d\) take?
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
    \Question[2] A number \(a\) is increased by 3 and this amount is then doubled. If the result of this is greater than \(a\), what values can \(a\) take?
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
\end{questions}
