Question

Which equation matches the solution set of {5} ?
2x - 20 = 30
x + x - 9 = 1 + x
x^2 - 10 = 15
3x/5 + 4 = 7

Answer 1

To determine which equation matches the solution set of {5}, we can solve each equation and check if \( x = 5 \) is a solution.

1. **Equation:** \( 2x - 20 = 30 \)

\[
2x - 20 = 30 \\
2x = 30 + 20 \\
2x = 50 \\
x = \frac{50}{2} \\
x = 25
\]

**Solution:** \( x = 25 \) (not \( 5 \))

2. **Equation:** \( x + x - 9 = 1 + x \)

\[
2x - 9 = 1 + x \\
2x - x = 1 + 9 \\
x = 10
\]

**Solution:** \( x = 10 \) (not \( 5 \))

3. **Equation:** \( x^2 - 10 = 15 \)

\[
x^2 - 10 = 15 \\
x^2 = 15 + 10 \\
x^2 = 25 \\
x = 5 \quad \text{or} \quad x = -5
\]

**Solution:** \( x = 5 \) (this works!)

4. **Equation:** \( \frac{3x}{5} + 4 = 7 \)

\[
\frac{3x}{5} = 7 - 4 \\
\frac{3x}{5} = 3 \\
3x = 3 \times 5 \\
3x = 15 \\
x = \frac{15}{3} \\
x = 5
\]

**Solution:** \( x = 5 \) (this also works!)

**Conclusion:**
Both equations \( x^2 - 10 = 15 \) and \( \frac{3x}{5} + 4 = 7 \) yield the solution \( x = 5 \). Thus, the equations that match the solution set of {5} are:

- \( x^2 - 10 = 15 \)
- \( \frac{3x}{5} + 4 = 7 \)

Answer 2

which one do you think is correct?

Answer 3

Both equations \( x^2 - 10 = 15 \) and \( \frac{3x}{5} + 4 = 7 \) correctly yield the solution \( x = 5 \). However, if you are looking for just one equation that matches the solution set of {5}, you could choose either.

Typically, if only one answer is needed, you might prefer the first one listed or the simplest one, which could be:

**The most straightforward choice is:**

- \( x^2 - 10 = 15 \)

This is a simple quadratic equation that leads directly to the solution \( x = 5 \).

If you're required to choose only one, I'd recommend using **\( x^2 - 10 = 15 \)** as the correct answer.