Answer
$\left(\dfrac{5}{8}, +\infty\right)$
Work Step by Step
Step $1$: Add two to both sides.
$$4x-2+2\gt \frac{1}{2}+2$$
$$4x\gt \frac{5}{2}$$
Step $2$: Divide both sides by $4$.
$$\dfrac{4x}{4}\gt \dfrac{\frac{5}{2}}{4}$$
$$4 \gt \dfrac{5}{2} \cdot \dfrac{1}{4}$$
$$x \gt \dfrac{5}{8}$$
To check, use $x=1$ and substitute it to $x$ in the given inequality to obtain:
$4(1)-2 \gt \frac{1}{2}\\
4-2 \gt \frac{1}{2}\\
2 \gt \frac{1}{2} \text{ which is true}$.
Thus, the solution set is $\left(\dfrac{5}{8}, +\infty\right)$.
