1. **State the problem:** Solve the linear equation $-3x - 4 = 8$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable $x$ by performing inverse operations (addition/subtraction, multiplication/division) on both sides. 3. **Step 1: Add 4 to both sides to cancel the $-4$ term:** $$-3x - 4 + 4 = 8 + 4$$ $$-3x = 12$$ 4. **Step 2: Divide both sides by $-3$ to isolate $x$:** $$\cancel{-3}x \div \cancel{-3} = 12 \div -3$$ $$x = -4$$ 5. **Final answer:** $$x = -4$$ This means the value of $x$ that satisfies the equation is $-4$.