Which of the following equations has the solution set x={−9/5, 3}?

Question

(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 equation has the solution set \( x = {-\frac{9}{5}, 3} \), we need to factor each equation and see which gives us these specific solutions.

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

   • Solutions:
     \[ x - 3 = 0 \implies x = 3 \]
     \[ 9x + 5 = 0 \implies 9x = -5 \implies x = -\frac{5}{9} \]
   • Solutions: \( x = {3, -\frac{5}{9}} \) (Not a match)

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

   • Solutions:
     \[ -3x = 0 \implies x = 0 \]
     \[ 5x + 9 = 0 \implies 5x = -9 \implies x = -\frac{9}{5} \]
   • Solutions: \( x = {0, -\frac{9}{5}} \) (Not a match)

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

   • Solutions:
     \[ x - 3 = 0 \implies x = 3 \]
     \[ 5x + 9 = 0 \implies 5x = -9 \implies x = -\frac{9}{5} \]
   • Solutions: \( x = {3, -\frac{9}{5}} \) (This matches)

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

   • Solutions:
     \[ x + 3 = 0 \implies x = -3 \]
     \[ 9x - 5 = 0 \implies 9x = 5 \implies x = \frac{5}{9} \]
   • Solutions: \( x = {-3, \frac{5}{9}} \) (Not a match)

After checking all options, the equation that matches the solution set \( x = {-\frac{9}{5}, 3} \) is:

(x−3)(5x+9)=0.