1. **State the problem:** Solve the linear equation $-2x - 3 = 5x + 11$ for $x$. 2. **Write down the equation:** $$-2x - 3 = 5x + 11$$ 3. **Goal:** Isolate $x$ on one side of the equation. 4. **Add $2x$ to both sides to move all $x$ terms to the right:** $$\cancel{-2x} - 3 + 2x = 5x + 11 + 2x$$ which simplifies to $$-3 = 7x + 11$$ 5. **Subtract 11 from both sides to isolate the term with $x$:** $$-3 - 11 = 7x + \cancel{11} - 11$$ which simplifies to $$-14 = 7x$$ 6. **Divide both sides by 7 to solve for $x$:** $$\frac{-14}{\cancel{7}} = \frac{7x}{\cancel{7}}$$ which simplifies to $$x = -2$$ **Final answer:** $$x = -2$$