12. \( \frac{50}{6}+\frac{3}{7}<\frac{5}{6} \)

Let's evaluate the inequality: \[ \frac{50}{6} + \frac{3}{7} < \frac{5}{6} \] ### Step 1: Simplify the Left Side First, calculate each fraction separately: 1. **\(\frac{50}{6}\)**: \[ \frac{50}{6} = 8.\overline{3} \quad \text{(approximately } 8.3333\text{)} \] 2. **\(\frac{3}{7}\)**: \[ \frac{3}{7} \approx 0.4286 \] Now, add them together: \[ \frac{50}{6} + \frac{3}{7} \approx 8.3333 + 0.4286 = 8.7619 \] ### Step 2: Simplify the Right Side \[ \frac{5}{6} \approx 0.8333 \] ### Step 3: Compare Both Sides Now, compare the two results: \[ 8.7619 \quad \text{(Left Side)} \quad \text{vs.} \quad 0.8333 \quad \text{(Right Side)} \] Clearly, \[ 8.7619 > 0.8333 \] ### Conclusion The original inequality states that: \[ \frac{50}{6} + \frac{3}{7} < \frac{5}{6} \] However, as we've calculated: \[ 8.7619 > 0.8333 \] **Therefore, the inequality is FALSE.**