1. **State the problem:** Solve the inequality $$-7 + 6x \neq -25$$ for $$x$$. 2. **Add 7 to both sides** to isolate the term with $$x$$: $$-7 + 6x + 7 \neq -25 + 7$$ $$6x \neq -18$$ 3. **Divide both sides by 6** to solve for $$x$$: $$x \neq \frac{-18}{6}$$ 4. **Simplify the fraction**: $$x \neq \cancel{\frac{-18}{6}}^{\frac{-3 \times 6}{1 \times 6}} = -3$$ **Final answer:** $$x \neq -3$$ This means $$x$$ can be any value except $$-3$$.