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

Question

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.