Correct Determine which of the following points are included in the solution set to the following linear inequality. $$ -3 x+3 y-8 $$ Answer $$ \left(4, \frac{4}{3}\right) $$ $$ (0,0) $$ $$ (-10,10) $$ $$ (10,-10) $$ $$ (8,4) $$

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Correct Determine which of the following points are included in the solution set to the following linear inequality. $$ -3 x+3 y>-8 $$ Answer $$ \left(4, \frac{4}{3}\right) $$ $$ (0,0) $$ $$ (-10,10) $$ $$ (10,-10) $$ $$ (8,4) $$

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 $$(-10, 10)$$.

Correct Determine which of the following points are included in the solution set to the following linear inequality. \[ -3 x+3 y>-8 \] Answer \( \left(4, \frac{4}{3}\right) \) \( (0,0) \) \( (-10,10) \) \( (10,-10) \) \( (8,4) \)

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