Question: 33 \over x = -3
1. **State the problem:** Solve the equation $$\frac{33}{x} = -3$$ for $$x$$.
2. **Formula and rules:** To solve for $$x$$ in a fraction equation $$\frac{a}{x} = b$$, multiply both sides by $$x$$ to get rid of the denominator, then divide both sides by $$b$$ to isolate $$x$$.
3. **Multiply both sides by $$x$$:**
$$33 = -3x$$
4. **Divide both sides by $$-3$$ to solve for $$x$$:**
$$x = \frac{33}{-3}$$
5. **Simplify the fraction:**
$$x = \frac{\cancel{33}}{\cancel{-3}} = -11$$
6. **Check the solution:** Substitute $$x = -11$$ back into the original equation:
$$\frac{33}{-11} = -3$$
which is true.
**Final answer:** $$x = -11$$