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

Question

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

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

−3x(5x+9)=0

Answer 1

To determine which of the given equations has the solution set \( x = {-95, 3} \), we need to find the values of \( x \) for which each equation is satisfied.

1. Equation: \( (x-3)(5x+9) = 0 \)

   • Set each factor to zero:
     • \( x - 3 = 0 \) gives \( x = 3 \).
     • \( 5x + 9 = 0 \) gives \( 5x = -9 \) or \( x = -\frac{9}{5} \).
   • Solution set: \( {3, -\frac{9}{5}} \)

2. Equation: \( (x+3)(9x-5) = 0 \)

   • Set each factor to zero:
     • \( x + 3 = 0 \) gives \( x = -3 \).
     • \( 9x - 5 = 0 \) gives \( 9x = 5 \) or \( x = \frac{5}{9} \).
   • Solution set: \( {-3, \frac{5}{9}} \)

3. Equation: \( (x-3)(9x+5) = 0 \)

   • Set each factor to zero:
     • \( x - 3 = 0 \) gives \( x = 3 \).
     • \( 9x + 5 = 0 \) gives \( 9x = -5 \) or \( x = -\frac{5}{9} \).
   • Solution set: \( {3, -\frac{5}{9}} \)

4. Equation: \( -3x(5x+9) = 0 \)

   • Set each factor to zero:
     • \( -3x = 0 \) gives \( x = 0 \).
     • \( 5x + 9 = 0 \) gives \( 5x = -9 \) or \( x = -\frac{9}{5} \).
   • Solution set: \( {0, -\frac{9}{5}} \)

From the calculations above, none of the equations produced the solution set \( {-95, 3} \).

The correct factors for this solution set would need to include \( x - 3 \) (which gives \( x = 3 \)) and \( x + 95 \) (which gives \( x = -95 \)), leading to an equation of the form: \[ (x - 3)(x + 95) = 0 \]

However, none of the provided options match this. Therefore, the answer is that none of the given equations has the solution set \( {-95, 3} \).