Which of the following equations has the solution set x={−95,3}

Question

?(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: \[ \boxed{-3x(5x + 9) = 0} \]