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 can analyze each option by checking the roots produced by setting the equations to zero.

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

   • Solutions:
     • \(x - 3 = 0 \rightarrow x = 3\)
     • \(9x + 5 = 0 \rightarrow 9x = -5 \rightarrow x = -\frac{5}{9}\)
   • Roots: \({3, -\frac{5}{9}}\)

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

   • Solutions:
     • \(-3x = 0 \rightarrow x = 0\)
     • \(5x + 9 = 0 \rightarrow 5x = -9 \rightarrow x = -\frac{9}{5}\)
   • Roots: \({0, -\frac{9}{5}}\)

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

   • Solutions:
     • \(x - 3 = 0 \rightarrow x = 3\)
     • \(5x + 9 = 0 \rightarrow 5x = -9 \rightarrow x = -\frac{9}{5}\)
   • Roots: \({3, -\frac{9}{5}}\) (Matches the solution set)

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

   • Solutions:
     • \(x + 3 = 0 \rightarrow x = -3\)
     • \(9x - 5 = 0 \rightarrow 9x = 5 \rightarrow x = \frac{5}{9}\)
   • Roots: \({-3, \frac{5}{9}}\)

From the evaluations above, the equation that has the solution set \( x = {-\frac{9}{5}, 3} \) is:

(x - 3)(5x + 9) = 0.