Correct

Determine which of the following points are included in the solution set to the following linear inequality.

Answer

Ask by Willis Carlson. in the United States

Jan 22,2025

Question

Correct

Determine which of the following points are included in the solution set to the following linear inequality.

Answer

Ask by Willis Carlson. in the United States

Jan 22,2025

UpStudy AI · Accepted Answer

To determine which points satisfy the linear inequality:

$$
-3x + 3y > -8
$$

**Step 1: Simplify the Inequality**

Divide both sides by 3 to simplify:

$$
-3x + 3y > -8 \quad \Rightarrow \quad -x + y > -\frac{8}{3} \quad \Rightarrow \quad y > x - \frac{8}{3}
$$

**Step 2: Test Each Point**

Let's evaluate each given point $$(x, y)$$ to see if it satisfies the inequality $$ y > x - \frac{8}{3} $$.

1. **$$\left(4, \frac{4}{3}\right)$$**
   $$
   y = \frac{4}{3} \quad \text{and} \quad x - \frac{8}{3} = 4 - \frac{8}{3} = \frac{4}{3}
   $$
   $$
   \frac{4}{3} > \frac{4}{3} \quad \text{(False)}
   $$
   **Does not satisfy the inequality.**

2. **$$(0, 0)$$**
   $$
   y = 0 \quad \text{and} \quad x - \frac{8}{3} = 0 - \frac{8}{3} = -\frac{8}{3}
   $$
   $$
   0 > -\frac{8}{3} \quad \text{(True)}
   $$
   **Satisfies the inequality.**

3. **$$(-10, 10)$$**
   $$
   y = 10 \quad \text{and} \quad x - \frac{8}{3} = -10 - \frac{8}{3} = -\frac{38}{3}
   $$
   $$
   10 > -\frac{38}{3} \quad \text{(True)}
   $$
   **Satisfies the inequality.**

4. **$$(10, -10)$$**
   $$
   y = -10 \quad \text{and} \quad x - \frac{8}{3} = 10 - \frac{8}{3} = \frac{22}{3}
   $$
   $$
   -10 > \frac{22}{3} \quad \text{(False)}
   $$
   **Does not satisfy the inequality.**

5. **$$(8, 4)$$**
   $$
   y = 4 \quad \text{and} \quad x - \frac{8}{3} = 8 - \frac{8}{3} = \frac{16}{3} \approx 5.33
   $$
   $$
   4 > \frac{16}{3} \quad \text{(False)}
   $$
   **Does not satisfy the inequality.**

**Conclusion**

The points that satisfy the inequality $$-3x + 3y > -8$$ are:

- $$(0, 0)$$
- $$(-10, 10)$$
The points that satisfy the inequality $$-3x + 3y > -8$$ are $$(0, 0)$$ and $$(-10, 10)$$.

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Determine which of the following points are included in the solution set to the following linear inequality.

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Correct Determine which of the following points are included in the solution set to the following linear inequality. Answer

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Determine which of the following points are included in the solution set to the following linear inequality.

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