G4.2 If $Q>0$ and satisfies $|3 Q-| 1-2 Q||=2$, find the value of $Q$.
$$
\begin{array}{l}
|3 Q-| 1-2 Q||=2 \\
3 Q-|1-2 Q|=2 \text { or } 3 Q-|1-2 Q|=-2 \\
3 Q-2=|1-2 Q| \text { or } 3 Q+2=|1-2 Q| \\
3 Q-2=1-2 Q \text { or } 3 Q-2=2 Q-1 \text { or } 3 Q+2=1-2 Q \text { or } 3 Q+2=2 Q-1 \\
Q=\frac{3}{5} \text { or } 1 \text { or }-\frac{1}{5} \text { (rejected) or }-3 \text { (rejected) }
\end{array}
$$
$Q=\frac{3}{5}$ or 1 or $-\frac{1}{5}$ (rejected) or -3 (rejected)
Check: when $Q=\frac{3}{5}$, LHS $=\left|\frac{9}{5}-\right| 1-\frac{6}{5}||=\frac{8}{5} \neq 2$, rejected
When $Q=1$, LHS $=|3-| 1-2||=2=$ RHS accepted
$$
\therefore Q=1
$$