Step 1: Simplify the left side of the inequality. $$3x - \frac{1}{4} \left(\frac{1}{2}\right) > \frac{1}{4} - x$$ Multiply the fractions on the left side: $$3x - \frac{1}{8} > \frac{1}{4} - x$$ Step 2: Gather all terms containing $x$ on one side and constant terms on the other side. Add $x$ to both sides of the inequality: $$3x + x - \frac{1}{8} > \frac{1}{4}$$ $$4x - \frac{1}{8} > \frac{1}{4}$$ Add $\frac{1}{8}$ to both sides of the inequality: $$4x > \frac{1}{4} + \frac{1}{8}$$ Step 3: Combine the constant terms on the right side. Find a common denominator for $\frac{1}{4}$ and $\frac{1}{8}$, which is 8. $$\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$$ Now add the fractions: $$4x > \frac{2}{8} + \frac{1}{8}$$ $$4x > \frac{3}{8}$$ Step 4: Solve for $x$. Divide both sides by 4: $$x > \frac{3}{8 \times 4}$$ $$x > \frac{3}{32}$$ Step 5: Express the solution as an interval. The inequality $x > \frac{3}{32}$ means that $x$ can be any value strictly greater than $\frac{3}{32}$. In interval notation, this is written as: $$\boxed{\left(\frac{3}{32}, \infty\right)}$$