Question

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

(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
left parenthesis x plus 3 right parenthesis left parenthesis 9 x minus 5 right parenthesis equals 0

−3x(5x+9)=0

Answer 1

To determine which equation has the solution set \( x = \{-\frac{9}{5}, 3\} \), we need to check each option one by one to see which one produces these roots.

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

To find the solutions, set each factor to zero:
- \(x - 3 = 0 \implies x = 3\)
- \(9x + 5 = 0 \implies 9x = -5 \implies x = -\frac{5}{9}\)

This gives us the solution set \( x = \{3, -\frac{5}{9}\} \), which does not match.

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

Set each factor to zero:
- \(x - 3 = 0 \implies x = 3\)
- \(5x + 9 = 0 \implies 5x = -9 \implies x = -\frac{9}{5}\)

This gives us the solution set \( x = \{3, -\frac{9}{5}\} \), which matches.

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

Set each factor to zero:
- \(x + 3 = 0 \implies x = -3\)
- \(9x - 5 = 0 \implies 9x = 5 \implies x = \frac{5}{9}\)

This gives us the solution set \( x = \{-3, \frac{5}{9}\} \), which does not match.

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

Set each factor to zero:
- \(-3x = 0 \implies x = 0\)
- \(5x + 9 = 0 \implies 5x = -9 \implies x = -\frac{9}{5}\)

This gives us the solution set \( x = \{0, -\frac{9}{5}\} \), which does not match.

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

**(x−3)(5x+9)=0**.