1. **State the problem:** We need to determine if each equation relating hours (h), days (d), months (m), and years (y) is always true, sometimes true, or false. 2. **Recall the definitions and conversions:** - 1 day = 24 hours - 1 year = 12 months - Number of days in a month varies (28 to 31 days) 3. **Analyze each equation:** **Equation 1: $d = 24h$** - This suggests 1 day equals 24 hours. - But $h$ represents hours, so if $h=1$, then $d=24$ days, which is incorrect. - Actually, 1 day = 24 hours means $h = 24d$, not $d = 24h$. - Therefore, this equation is **false**. **Equation 2: $m = 12y$** - This suggests months equal 12 times years. - Since 1 year = 12 months, $m = 12y$ is **always true**. **Equation 3: $d = 31m$** - This suggests days equal 31 times months. - Months have varying days: 28, 29, 30, or 31. - So, $d = 31m$ is **sometimes true** (only for months with 31 days). 4. **Summary:** - $d = 24h$ is false. - $m = 12y$ is always true. - $d = 31m$ is sometimes true. 5. **Final answers:** - $d = 24h$: False - $m = 12y$: Always true - $d = 31m$: Sometimes true