Let's analyze the given inequality [tex]\( y \leq \frac{7}{x} - 3 \)[/tex].
### Step-by-Step Solution:
1. Identify the Inequality Type:
- The inequality given is [tex]\( y \leq \frac{7}{x} - 3 \)[/tex].
- The symbol [tex]\( \leq \)[/tex] indicates that we are dealing with a "less than or equal to" inequality.
2. Determine the Boundary Line:
- The boundary line for the inequality [tex]\( y \leq \frac{7}{x} - 3 \)[/tex] is [tex]\( y = \frac{7}{x} - 3 \)[/tex].
3. Solid or Dashed Line:
- For inequalities involving [tex]\( \leq \)[/tex] or [tex]\( \geq \)[/tex] (less than or equal to, or greater than or equal to), the boundary line is solid because points on the line satisfy the inequality.
- If the inequality did not have the equal part (just < or >), the boundary line would be dashed, indicating points on the line do not satisfy the inequality.
4. Shading the Region:
- The inequality is [tex]\( y \leq \frac{7}{x} - 3 \)[/tex], which means [tex]\( y \)[/tex] is less than or equal to the boundary line.
- Therefore, the region on the graph that satisfies this inequality is below the line [tex]\( y = \frac{7}{x} - 3 \)[/tex].
### Conclusion:
The correct description of the shaded region for the inequality [tex]\( y \leq \frac{7}{x} - 3 \)[/tex] is:
The shaded region would be below a solid line.
Therefore, the final answer is:
The shaded region would be below a solid line.
