Question

Which equation matches the solution set of {5}?(1 point)
Responses

x+x−9=1+x
x plus x minus 9 is equal to 1 plus x

3x5+4=7
3 x over 5 plus 4 is equal to 7

x2+10=15
x squared plus 10 is equal to 15

2x−20=30
2 x minus 20 is equal to 30

Answer 1

To determine which equation matches the solution set of {5}, we can solve each equation for \( x \) and see which one yields \( x = 5 \).

1. **Equation:** \( x + x - 9 = 1 + x \)
- Simplifying:
\[
2x - 9 = 1 + x
\]
\[
2x - x = 1 + 9
\]
\[
x = 10 \quad \text{(Not 5)}
\]

2. **Equation:** \( \frac{3x}{5} + 4 = 7 \)
- Simplifying:
\[
\frac{3x}{5} = 7 - 4
\]
\[
\frac{3x}{5} = 3
\]
\[
3x = 15
\]
\[
x = 5 \quad \text{(Matches)}
\]

3. **Equation:** \( x^2 + 10 = 15 \)
- Simplifying:
\[
x^2 = 15 - 10
\]
\[
x^2 = 5
\]
\[
x = \sqrt{5} \quad \text{or} \quad x = -\sqrt{5} \quad \text{(Not 5)}
\]

4. **Equation:** \( 2x - 20 = 30 \)
- Simplifying:
\[
2x = 30 + 20
\]
\[
2x = 50
\]
\[
x = 25 \quad \text{(Not 5)}
\]

The equation that has the solution set of {5} is:
- **Response:** \( \frac{3x}{5} + 4 = 7 \)