Question

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

x2−10=15
x squared minus 10 equals 15

x+x−9=1+x
x plus x minus 9 equals 1 plus x

2x−20=30
2 x minus 20 equals 30

3x5+4=7

Answer 1

To find which equation has the solution set of {5}, we need to substitute \( x = 5 \) into each equation and see if the equation holds true.

1. **Equation 1:** \( x^2 - 10 = 15 \)

Substitute \( x = 5 \):
\[
5^2 - 10 = 25 - 10 = 15 \quad \text{(True)}
\]

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

Substitute \( x = 5 \):
\[
5 + 5 - 9 = 1 + 5 \\
1 = 6 \quad \text{(False)}
\]

3. **Equation 3:** \( 2x - 20 = 30 \)

Substitute \( x = 5 \):
\[
2(5) - 20 = 30 \\
10 - 20 = 30 \\
-10 = 30 \quad \text{(False)}
\]

4. **Equation 4:** \( 3x + 4 = 7 \)

Substitute \( x = 5 \):
\[
3(5) + 4 = 7 \\
15 + 4 = 7 \\
19 = 7 \quad \text{(False)}
\]

Only the first equation \( x^2 - 10 = 15 \) holds true when \( x = 5 \). Therefore, the equation that matches the solution set of {5} is:

**x^2 - 10 = 15**.