1. **State the problem:** Solve the inequality $$-7x - \left(-5x + \frac{1}{4}\right) \leq -1$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign: $$-7x + 5x - \frac{1}{4} \leq -1$$. 3. **Combine like terms:** $$(-7x + 5x) - \frac{1}{4} \leq -1$$ $$-2x - \frac{1}{4} \leq -1$$. 4. **Isolate the variable term:** Add $\frac{1}{4}$ to both sides: $$-2x - \frac{1}{4} + \frac{1}{4} \leq -1 + \frac{1}{4}$$ $$-2x \leq -\frac{3}{4}$$. 5. **Divide both sides by $-2$ to solve for $x$:** Remember, dividing by a negative number reverses the inequality sign: $$x \geq \frac{-\frac{3}{4}}{-2}$$ $$x \geq \frac{3}{4} \times \frac{1}{2}$$ $$x \geq \frac{3}{8}$$. **Final answer:** $$x \geq \frac{3}{8}$$. This means $x$ can be any number greater than or equal to $\frac{3}{8}$.