Determine which of the following points are included in the solution set to the following linear inequality. $$ \begin{array}{l}-3 x+2 y \geq-6\end{array} $$ $$ \begin{array}{l}\square(4,-5) \ \text { Answer } \ \square(0,0) \ \square\left(3, \frac{3}{2}\right) \ \square(7,-7)\end{array} $$

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To determine which points satisfy the inequality:

$$
-3x + 2y \geq -6
$$

Let's evaluate each point by substituting the $$ x $$ and $$ y $$ values into the inequality.

1. **Point (4, -5):**
   $$
   -3(4) + 2(-5) = -12 - 10 = -22
   $$
   $$
   -22 \geq -6 \quad \text{(False)}
   $$
   **Does not satisfy** the inequality.

2. **Point (0, 0):**
   $$
   -3(0) + 2(0) = 0
   $$
   $$
   0 \geq -6 \quad \text{(True)}
   $$
   **Satisfies** the inequality.

3. **Point $$\left(3, \frac{3}{2}\right)$$:**
   $$
   -3(3) + 2\left(\frac{3}{2}\right) = -9 + 3 = -6
   $$
   $$
   -6 \geq -6 \quad \text{(True)}
   $$
   **Satisfies** the inequality.

4. **Point (7, -7):**
   $$
   -3(7) + 2(-7) = -21 - 14 = -35
   $$
   $$
   -35 \geq -6 \quad \text{(False)}
   $$
   **Does not satisfy** the inequality.

### Summary of Points:

- ☐ (4, -5)
- ☑ (0, 0)
- ☑ $$\left(3, \frac{3}{2}\right)$$
- ☐ (7, -7)

**Points that satisfy the inequality:** $$(0, 0)$$ and $$\left(3, \frac{3}{2}\right)$$.
The points that satisfy the inequality are (0, 0) and $$\left(3, \frac{3}{2}\right)$$.

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

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