Question(b) By writing $|x| \geq a$ in the equivalent for $x \geq a$ or $x \leq-a$, determine the solution set for $$\left|\frac{x-3}{2 x-1}\right| \geq \frac{1}{2}$$ [6 marks]

Studdy Solution
Consider any restrictions on the domain of the function:
The expression $\frac{x-3}{2x-1}$ is undefined when the denominator is zero, i.e., $2x - 1 = 0$, which gives $x = \frac{1}{2}$.
Therefore, the solution set must exclude $x = \frac{1}{2}$.
The final solution set is:
$$x \leq \frac{7}{4}, \, x \neq \frac{1}{2}$$
The solution set is:
$$\boxed{x \leq \frac{7}{4}, \, x \neq \frac{1}{2}}$$