Determine which of the following points are included in the solution set to the following linear inequality. $$ \begin{array}{l}4 x+5 y

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Determine which of the following points are included in the solution set to the following linear inequality. $$ \begin{array}{l}4 x+5 y<11\end{array} $$ Answer $$ \square(4,-1) $$ $$ \square(9,-9) $$ $$ \square(0,0) $$ $$ \square(3,2) $$ $$ \square(9,4) $$

UpStudy AI · Accepted Answer

To determine which points satisfy the inequality $$ 4x + 5y < 11 $$, we'll substitute each point into the inequality and check if the statement holds true.

1. **Point (4, -1):**
   $$
   4(4) + 5(-1) = 16 - 5 = 11 \quad \text{which is not less than 11.}
   $$
   **Does not satisfy the inequality.**

2. **Point (9, -9):**
   $$
   4(9) + 5(-9) = 36 - 45 = -9 \quad \text{which is less than 11.}
   $$
   **Satisfies the inequality.**

3. **Point (0, 0):**
   $$
   4(0) + 5(0) = 0 + 0 = 0 \quad \text{which is less than 11.}
   $$
   **Satisfies the inequality.**

4. **Point (3, 2):**
   $$
   4(3) + 5(2) = 12 + 10 = 22 \quad \text{which is not less than 11.}
   $$
   **Does not satisfy the inequality.**

5. **Point (9, 4):**
   $$
   4(9) + 5(4) = 36 + 20 = 56 \quad \text{which is not less than 11.}
   $$
   **Does not satisfy the inequality.**

**Summary of Solution Set:**

- $$ \square(4, -1) $$ **❌**
- $$ \square(9, -9) $$ **✅**
- $$ \square(0, 0) $$ **✅**
- $$ \square(3, 2) $$ **❌**
- $$ \square(9, 4) $$ **❌**

**Included Points in the Solution Set:**

- $$ (9, -9) $$
- $$ (0, 0) $$
The points that satisfy the inequality $$ 4x + 5y < 11 $$ are $$ (9, -9) $$ and $$ (0, 0) $$.

Determine which of the following points are included in the solution set to the following linear inequality. \[ \begin{array}{l}4 x+5 y<11\end{array} \] Answer \( \square(4,-1) \) \( \square(9,-9) \) \( \square(0,0) \) \( \square(3,2) \) \( \square(9,4) \)

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