Question

Which equations have the solution set of {1/4, −5}
?

Select all that apply.

(3 points)
Responses

(4x − 1)(x+5)=0
(4x − 1)(x+5)=0

(8x - 2)(x + 5) = 0
(8x - 2)(x + 5) = 0

(2x - 8)(x - 5) = 0
(2x - 8)(x - 5) = 0

(x − 14)(x − 5) = 0
(x − 14)(x − 5) = 0

(4x + 2)(x + 5) = 0
(4x + 2)(x + 5) = 0

(x − 14)(x + 5) = 0
(x − 14)(x + 5) = 0

(x + 14)(x + 5) = 0

Answer 1

To determine which equations have the solution set \(\{ \frac{1}{4}, -5 \}\), we need to check each equation by solving for \(x\).

1. **Equation: \((4x - 1)(x + 5) = 0\)**

- Set \(4x - 1 = 0\):

\(4x = 1\)

\(x = \frac{1}{4}\)

- Set \(x + 5 = 0\):

\(x = -5\)

- **Solutions**: \(\{ \frac{1}{4}, -5 \}\)

2. **Equation: \((8x - 2)(x + 5) = 0\)**

- Set \(8x - 2 = 0\):

\(8x = 2\)

\(x = \frac{1}{4}\)

- Set \(x + 5 = 0\):

\(x = -5\)

- **Solutions**: \(\{ \frac{1}{4}, -5 \}\)

3. **Equation: \((2x - 8)(x - 5) = 0\)**

- Set \(2x - 8 = 0\):

\(2x = 8\)

\(x = 4\)

- Set \(x - 5 = 0\):

\(x = 5\)

- **Solutions**: \(\{ 4, 5 \}\) (not valid)

4. **Equation: \((x - 14)(x - 5) = 0\)**

- Set \(x - 14 = 0\):

\(x = 14\)

- Set \(x - 5 = 0\):

\(x = 5\)

- **Solutions**: \(\{ 14, 5 \}\) (not valid)

5. **Equation: \((4x + 2)(x + 5) = 0\)**

- Set \(4x + 2 = 0\):

\(4x = -2\)

\(x = -\frac{1}{2}\)

- Set \(x + 5 = 0\):

\(x = -5\)

- **Solutions**: \(\{ -\frac{1}{2}, -5 \}\) (not valid)

6. **Equation: \((x - 14)(x + 5) = 0\)**

- Set \(x - 14 = 0\):

\(x = 14\)

- Set \(x + 5 = 0\):

\(x = -5\)

- **Solutions**: \(\{ 14, -5 \}\) (not valid)

7. **Equation: \((x + 14)(x + 5) = 0\)**

- Set \(x + 14 = 0\):

\(x = -14\)

- Set \(x + 5 = 0\):

\(x = -5\)

- **Solutions**: \(\{ -14, -5 \}\) (not valid)

Based on the analysis, the equations that have the solution set \(\{ \frac{1}{4}, -5 \}\) are:

- \((4x - 1)(x + 5) = 0\)
- \((8x - 2)(x + 5) = 0\)

So the responses with valid solution sets are:

- \((4x - 1)(x + 5) = 0\)
- \((8x - 2)(x + 5) = 0\)