1. **State the problem:** Solve the inequality $$3x - (-5) \leq -7$$. 2. **Rewrite the inequality:** Subtracting a negative is the same as adding, so rewrite as $$3x + 5 \leq -7$$. 3. **Isolate the term with $x$:** Subtract 5 from both sides: $$3x + 5 - \cancel{5} \leq -7 - \cancel{5}$$ which simplifies to $$3x \leq -12$$. 4. **Solve for $x$:** Divide both sides by 3. Since 3 is positive, the inequality direction stays the same: $$\frac{3x}{\cancel{3}} \leq \frac{-12}{\cancel{3}}$$ which simplifies to $$x \leq -4$$. 5. **Interpretation:** The solution is all $x$ values less than or equal to $-4$. 6. **Check boundary:** Substitute $x = -4$ into the original inequality: $$3(-4) - (-5) = -12 + 5 = -7$$ which satisfies $$-7 \leq -7$$, so the boundary is included. **Final answer:** $$x \leq -4$$.