Question

Which of the following equations has the solution set x={−9/5,3} ?(1 point) 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 find out which of the given equations has the solution set \( x = {-\frac{9}{5}, 3} \), we can test each equation to see if it results in these solutions.

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

   • Setting each factor to zero:
     • \(-3x = 0 \Rightarrow x = 0\)
     • \(5x + 9 = 0 \Rightarrow 5x = -9 \Rightarrow x = -\frac{9}{5}\)
   • Solutions: \(x = 0\) and \(x = -\frac{9}{5}\) (not a match).

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

   • Setting each factor to zero:
     • \(x - 3 = 0 \Rightarrow x = 3\)
     • \(9x + 5 = 0 \Rightarrow 9x = -5 \Rightarrow x = -\frac{5}{9}\)
   • Solutions: \(x = 3\) and \(x = -\frac{5}{9}\) (not a match).

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

   • Setting each factor to zero:
     • \(x - 3 = 0 \Rightarrow x = 3\)
     • \(5x + 9 = 0 \Rightarrow 5x = -9 \Rightarrow x = -\frac{9}{5}\)
   • Solutions: \(x = 3\) and \(x = -\frac{9}{5}\) (this is a match!).

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

   • Setting each factor to zero:
     • \(x + 3 = 0 \Rightarrow x = -3\)
     • \(9x - 5 = 0 \Rightarrow 9x = 5 \Rightarrow x = \frac{5}{9}\)
   • Solutions: \(x = -3\) and \(x = \frac{5}{9}\) (not a match).

The only equation with the solution set \( x = {-\frac{9}{5}, 3} \) is:

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