Sketch the graph with equation
$$y = | 3 x - 2 a |$$
where \(a\) is a positive constant.
State the coordinates of each point where the graph cuts or meets the coordinate axes.
Solve, in terms of \(a\), the inequality
$$| 3 x - 2 a | \leqslant x + a$$
Given that \(| 3 x - 2 a | \leqslant x + a\)
find, in terms of \(a\), the range of possible values of \(\mathrm { g } ( x )\), where
$$\mathrm { g } ( x ) = 5 a - \left| \frac { 1 } { 2 } a - x \right|$$