Question

Which of the following equations has the solution set x={−95,3}
?(1 point)
Responses

(x−3)(5x+9)=0
left parenthesis x minus 3 right parenthesis left parenthesis 5 x plus 9 right parenthesis equals 0

(x+3)(9x−5)=0
left parenthesis x plus 3 right parenthesis left parenthesis 9 x minus 5 right parenthesis equals 0

−3x(5x+9)=0
negative 3 x left parenthesis 5 x plus 9 right parenthesis equals 0

(x−3)(9x+5)=0

Answer 1

To determine which equation has the solution set \( x = \{-95, 3\} \), we need to find an equation that equals zero when \( x = -95 \) and \( x = 3 \).

### Checking each equation:

1. **Equation:** \( (x - 3)(5x + 9) = 0 \)
- For \( x = -95 \):
\[
-95 - 3 = -98 \quad (\text{not a solution})
\]
- For \( x = 3 \):
\[
3 - 3 = 0 \quad (\text{solution})
\]
- **Not valid.**

2. **Equation:** \( (x + 3)(9x - 5) = 0 \)
- For \( x = -95 \):
\[
-95 + 3 = -92 \quad (\text{not a solution})
\]
- For \( x = 3 \):
\[
3 + 3 = 6 \quad (\text{not a solution})
\]
- **Not valid.**

3. **Equation:** \( -3x(5x + 9) = 0 \)
- For \( x = -95 \):
\[
-3(-95)(5(-95) + 9) = 0 \quad (\text{solution})
\]
- For \( x = 3 \):
\[
-3(3)(5(3) + 9) = 0 \quad (\text{solution})
\]
- **Valid!**

4. **Equation:** \( (x - 3)(9x + 5) = 0 \)
- For \( x = -95 \):
\[
-95 - 3 = -98 \quad (\text{not a solution})
\]
- For \( x = 3 \):
\[
3 - 3 = 0 \quad (\text{solution})
\]
- **Not valid.**

### Conclusion
The equation that has the solution set \( x = \{-95, 3\} \) is:
\[
\boxed{-3x(5x + 9) = 0}
\]