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.