16. Reasoning If you are given a true equation and you multiply each side by the same number, the resulting equation is also a true equation. If you are given a false equation and you multiply each side by the same number, will the resulting equation be a true equation or a false equation? Give an example to explain.

To understand the effect of multiplying both sides of a false equation by the same number, let's break it down step by step. 1. **Definition of a False Equation**: A false equation is one where the two sides do not equal each other. For example, consider the equation \(2 = 3\). This is false because 2 is not equal to 3. 2. **Multiplying Both Sides by the Same Number**: If we multiply both sides of a false equation by the same non-zero number, the relationship between the two sides remains unchanged. This means that if the original equation is false, the new equation will also be false. 3. **Example**: - Start with the false equation: \[ 2 = 3 \] - Multiply both sides by 4: \[ 4 \cdot 2 = 4 \cdot 3 \] - This simplifies to: \[ 8 = 12 \] - The new equation \(8 = 12\) is still false because 8 is not equal to 12. 4. **Conclusion**: Therefore, if you multiply each side of a false equation by the same number, the resulting equation will also be false. This reasoning holds true as long as the number you are multiplying by is not zero, since multiplying by zero would make both sides equal to zero, which is a special case.