the container is 5/8 full.
Step-by-step explanation:
The given inequality, \( \frac{3}{8}x + 2 > 3 \), describes the situation where the lab manager prefers at least 3 liters of empty space in the container after discarding 2 liters of waste when the container is 5/8 full.
To understand this inequality, we can break it down step by step:
1. Start by subtracting 2 from both sides of the inequality:
\( \frac{3}{8}x + 2 - 2 > 3 - 2 \)
\( \frac{3}{8}x > 1 \)
2. Then, multiply both sides by 8 to eliminate the fraction:
\( 8(\frac{3}{8}x) > 8 \times 1 \)
\( 3x > 8 \)
3. Finally, divide by 3 to isolate x:
\( \frac{3x}{3} > \frac{8}{3} \)
\( x > \frac{8}{3} \)
