https://file.aiquickdraw.com/mathbot/file/1728509558570jax1qud8.jpg

Let's work through the inequalities given that \( x = -5 \) and \( y = 8 \).

The inequalities are all of the form:

\[
5x + 6y \ \text{inequality symbol} \ -10
\]

### Step 1: Substitute \( x = -5 \) and \( y = 8 \) into the expression \( 5x + 6y \).

\[
5(-5) + 6(8) = -25 + 48 = 23
\]

Now, we check this value (23) against each inequality.

### Step 2: Check the inequalities:

1. **For \( 5x + 6y < -10 \)**:
   \[
   23 < -10 \quad (\text{False})
   \]
   **Conclusion**: Not a solution.

2. **For \( 5x + 6y \leq -10 \)**:
   \[
   23 \leq -10 \quad (\text{False})
   \]
   **Conclusion**: Not a solution.

3. **For \( 5x + 6y \geq -10 \)**:
   \[
   23 \geq -10 \quad (\text{True})
   \]
   **Conclusion**: This is a solution.

4. **For \( 5x + 6y > -10 \)**:
   \[
   23 > -10 \quad (\text{True})
   \]
   **Conclusion**: This is a solution.

### Final conclusions:

- \( 5x + 6y < -10 \) → Not a solution.
- \( 5x + 6y \leq -10 \) → Not a solution.
- \( 5x + 6y \geq -10 \) → Solution.
- \( 5x + 6y > -10 \) → Solution.

Would you like further details or have any questions?

Here are some related questions to explore:
1. How do we solve inequalities with two variables?
2. What is the difference between strict and non-strict inequalities?
3. How can graphing inequalities help in understanding solutions?
4. What happens when the inequality signs flip?
5. How do changes in \( x \) and \( y \) affect the inequality solutions?

**Tip**: Always substitute values step-by-step to avoid mistakes when solving inequalities!

Is x = -5 and y = 8 a solution of the following inequalities? (5x + 6y < -10, 5x + 6y ≤ -10, 5x + 6y ≥ -10, 5x + 6y > -10)

Learn how to determine whether the values x = -5 and y = 8 solve the inequalities 5x + 6y < -10, ≤ -10, ≥ -10, and > -10. This solution covers substitution in linear inequalities and checks against each condition step by step.

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