1. **State the problem:** Determine if the numbers 38, 58, and 76 are all multiples of 19. 2. **Recall the definition:** A number $n$ is a multiple of 19 if there exists an integer $k$ such that $n = 19k$. 3. **Check each number:** - For 38: Calculate $\frac{38}{19} = 2$ which is an integer, so 38 is a multiple of 19. - For 58: Calculate $\frac{58}{19} = \cancel{\frac{58}{19}} = \frac{58}{19} = 3.0526...$ which is not an integer, so 58 is not a multiple of 19. - For 76: Calculate $\frac{76}{19} = 4$ which is an integer, so 76 is a multiple of 19. 4. **Conclusion:** Since 58 is not a multiple of 19, the statement "38, 58, 76 are all multiples of 19" is **false**.