Question: support your conclusion.
$$\frac{33}{x} = -3$$
1. **State the problem:** We need to solve the equation $$\frac{33}{x} = -3$$ and verify the solution.
2. **Solve for $$x$$:** Multiply both sides by $$x$$ to eliminate the denominator:
$$33 = -3x$$
3. **Isolate $$x$$:** Divide both sides by $$-3$$:
$$x = \frac{33}{-3}$$
4. **Simplify the fraction:**
$$x = \cancel{\frac{33}{\cancel{3}}} \times \frac{1}{-1} = -11$$
5. **Check the solution:** Substitute $$x = -11$$ back into the original equation:
$$\frac{33}{-11} = -3$$
Simplify:
$$-3 = -3$$ which is true.
6. **Test a false value:** Choose $$x = 11$$ and substitute:
$$\frac{33}{11} = 3$$
This simplifies to:
$$3 = -3$$ which is false.
**Final conclusion:** The equation has one solution, $$x = -11$$, which makes the equation true. Other values, such as $$x = 11$$, make the equation false.