Question

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

(x−3)(9x+5)=0
open paren x minus 3 close paren times open paren 9 x plus 5 close paren is equal to 0

−3x(5x+9)=0
negative 3 x open paren 5 x plus 9 close paren is equal to 0

(x−3)(5x+9)=0
open paren x minus 3 close paren times open paren 5 x plus 9 close paren is equal to 0

(x+3)(9x−5)=0

Answer 1

To determine which of the given equations has the solution set \( x = \{-95, 3\} \), we can analyze each equation.

1. **Equation:** \( (x−3)(9x+5)=0 \)
- Solutions: \( x - 3 = 0 \) gives \( x = 3 \)
- \( 9x + 5 = 0 \) gives \( x = -\frac{5}{9} \)
- **Solution set:** \( \{3, -\frac{5}{9}\} \) (not correct)

2. **Equation:** \( -3x(5x+9)=0 \)
- Solutions: \( -3x = 0 \) gives \( x = 0 \)
- \( 5x + 9 = 0 \) gives \( x = -\frac{9}{5} \)
- **Solution set:** \( \{0, -\frac{9}{5}\} \) (not correct)

3. **Equation:** \( (x−3)(5x+9)=0 \)
- Solutions: \( x - 3 = 0 \) gives \( x = 3 \)
- \( 5x + 9 = 0 \) gives \( x = -\frac{9}{5} \)
- **Solution set:** \( \{3, -\frac{9}{5}\} \) (not correct)

4. **Equation:** \( (x+3)(9x−5)=0 \)
- Solutions: \( x + 3 = 0 \) gives \( x = -3 \)
- \( 9x - 5 = 0 \) gives \( x = \frac{5}{9} \)
- **Solution set:** \( \{-3, \frac{5}{9}\} \) (not correct)

None of the equations listed directly leads to the solution set \( x = \{-95, 3\} \). The correct equations would need to have solutions that satisfy these exact values.

To construct an equation that yields \( x = -95 \) and \( x = 3 \):

1. The factors corresponding to the roots \( x + 95 \) and \( x - 3 \) lead to the equation:
\[
(x + 95)(x - 3) = 0
\]

This indicates that none of the listed equations produces the desired solution set. The appropriate equation would be:
\[
(x + 95)(x - 3) = 0
\]

However, this equation is not among the options given.