Which of the following equations has the solution set x={−9/5,3} ?(1 point)

Question

Responses

−3x(5x+9)=0
negative 3 x left parenthesis 5 x plus 9 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

(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

Answer 1

To determine which equation has the solution set \( x = {-9/5, 3} \), we need to identify which of the provided equations yields these roots.

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

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

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

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

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

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

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

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

From this analysis, the only equation that produces the solution set \( {-9/5, 3} \) is the third equation: \( (x-3)(5x+9)=0 \).