Question

which of the following equations has the solution set x = {-9/5, 3}

Answer 1

the specific equations
a. (x - 3) (9x + 5) = 0
b. -3x (5x + 9) = 0
c. (x - 3) (5x + 9) = 0
d. (x + 3) (9x - 5) = 0

Answer 2

To determine which equation has the solution set \( x = \left\{-\frac{9}{5}, 3\right\} \), we can create a polynomial that has these roots. If \( x = -\frac{9}{5} \) and \( x = 3 \) are the roots, then we can use the factored form of a polynomial.

1. The factors corresponding to the roots will be:
- For \( x = -\frac{9}{5} \): \( x + \frac{9}{5} \)
- For \( x = 3 \): \( x - 3 \)

2. We can express the polynomial as:
\[
P(x) = (x + \frac{9}{5})(x - 3)
\]

3. To eliminate the fraction, we can multiply the entire equation by 5:
\[
5P(x) = 5\left(x + \frac{9}{5}\right)(x - 3) = (5x + 9)(x - 3)
\]

4. Now, let's expand this:
\[
= 5x^2 - 15x + 9x - 27
\]
\[
= 5x^2 - 6x - 27
\]

Thus, the polynomial equation \( 5x^2 - 6x - 27 = 0 \) has the solution set \( x = \left\{-\frac{9}{5}, 3\right\} \).

If you have specific equations listed, please provide them, and we can determine which one matches this polynomial.

Answer 3

To find out which equation has the solution set \( x = \left\{-\frac{9}{5}, 3\right\} \), we'll solve each of the given equations:

### a. \( (x - 3)(9x + 5) = 0 \)
- Setting each factor to zero:
- \( x - 3 = 0 \) gives \( x = 3 \)
- \( 9x + 5 = 0 \) gives \( 9x = -5 \) or \( x = -\frac{5}{9} \)

**Solution set:** \( \{3, -\frac{5}{9}\} \)

### b. \( -3x(5x + 9) = 0 \)
- Setting each factor to zero:
- \( -3x = 0 \) gives \( x = 0 \)
- \( 5x + 9 = 0 \) gives \( 5x = -9 \) or \( x = -\frac{9}{5} \)

**Solution set:** \( \{0, -\frac{9}{5}\} \)

### c. \( (x - 3)(5x + 9) = 0 \)
- Setting each factor to zero:
- \( x - 3 = 0 \) gives \( x = 3 \)
- \( 5x + 9 = 0 \) gives \( 5x = -9 \) or \( x = -\frac{9}{5} \)

**Solution set:** \( \{3, -\frac{9}{5}\} \)

### d. \( (x + 3)(9x - 5) = 0 \)
- Setting each factor to zero:
- \( x + 3 = 0 \) gives \( x = -3 \)
- \( 9x - 5 = 0 \) gives \( 9x = 5 \) or \( x = \frac{5}{9} \)

**Solution set:** \( \{-3, \frac{5}{9}\} \)

### Summary of Solution Sets:
- a. \( \{3, -\frac{5}{9}\} \)
- b. \( \{0, -\frac{9}{5}\} \)
- c. \( \{3, -\frac{9}{5}\} \)
- d. \( \{-3, \frac{5}{9}\} \)

The equations that yield the solution set \( x = \left\{-\frac{9}{5}, 3\right\} \) is:

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