The inequality given is:

\[
6x - y \geq -5
\]

### Solution
To interpret this inequality:

1. **Isolate \( y \):** Rearranging the inequality to solve for \( y \) in terms of \( x \):
   \[
   -y \geq -6x - 5
   \]
   Multiply both sides by \(-1\) (which reverses the inequality sign):
   \[
   y \leq 6x + 5
   \]

2. **Graph Interpretation:** 
   - This inequality represents the region on a graph where \( y \) is less than or equal to \( 6x + 5 \).
   - The boundary line, \( y = 6x + 5 \), will be solid because the inequality includes equality (≥ or ≤).
   - Shade the region below this line to represent \( y \leq 6x + 5 \).

Would you like further details on graphing or any other aspects?

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### Related Questions:
1. How would you solve \(6x - y < -5\)?
2. How would this inequality change if it was \(6x + y \geq -5\)?
3. What is the slope and y-intercept of \(y = 6x + 5\)?
4. How do we graph inequalities with \(\geq\) and \(>\) signs?
5. How do we test if a point lies within the solution set of this inequality?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing both sides by a negative.

Learn how to solve and graph the linear inequality 6x - y ≥ -5. This solution involves rearranging the inequality, graphing the boundary line y = 6x + 5, and shading the correct region. Suitable for students in Grades 8-10, this problem covers key algebraic concepts and graph interpretation.

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