Question: User: -5x - 16 = 8x - 3
1. **State the problem:** Solve the linear equation $$-5x - 16 = 8x - 3$$ for $x$.
2. **Write down the formula and rules:** To solve for $x$, we want to isolate $x$ on one side of the equation. We can do this by adding or subtracting terms on both sides and then dividing if necessary.
3. **Add $5x$ to both sides to move all $x$ terms to the right:**
$$-5x - 16 + 5x = 8x - 3 + 5x$$
which simplifies to
$$-16 = 13x - 3$$
4. **Add $3$ to both sides to move constants to the left:**
$$-16 + 3 = 13x - 3 + 3$$
which simplifies to
$$-13 = 13x$$
5. **Divide both sides by $13$ to solve for $x$:**
$$\frac{-13}{\cancel{13}} = \frac{13x}{\cancel{13}}$$
which simplifies to
$$x = -1$$
6. **Final answer:**
$$x = -1$$