Sometimes instead of having an equation such as $3x + 7 = 22$, we have many variables such as $ax + b = c$. But our algebraic rules still apply and we can treat these letters the same way as we would treat the numbers:
\begin{enumerate}
    \item Subtract $b$ from both sides
    \item Divide both sides by $a$
\end{enumerate}
Which would have been the same as subtracting both sides by $7$ and then dividing by $3$ in our \textit{numerical} example.

This type of mathematics - rearranging for a variable even when the other variables are unknown is very helpful in the mathematics that you will soon do. Practise this skill thoroughly:

\begin{examplebox}
    \subsection{Examples:}
    \begin{questions}
        \Question[1] Rewrite $a(x+b) = c$ in terms of $x$.
            \begin{solutionordottedlines}[2cm]
\[
x=\frac{c-a b}{a}
\]
            \end{solutionordottedlines}
        \Question[1] Solve $mx-n =nx+m$ for $x$.
            \begin{solutionordottedlines}[2cm]
                \[x =\frac{m+n}{m-n}\]
            \end{solutionordottedlines}
    \end{questions}
\end{examplebox}

\begin{exercisebox}
    \subsection{Exercises:}
    \begin{questions}
        \question Solve each of these equations for \(x\).
        \begin{parts}\begin{multicols}{2}
            \part \[x+b=c\]
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \[p-x=q\]
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \[c x=b\]
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \[a(x+b)=c\]
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \[\frac{x}{a}=b\]
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \[\frac{x}{a}+b=c\]
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \[\frac{a x}{b}+c=d\]
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \[\frac{m x-n}{n}=m\]
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \[\frac{x}{a}-\frac{a}{b}=b\]
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \[a x+b=c x+d\]
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \[a(x+b)=c x+d\]
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
    \end{questions}
\end{exercisebox}

