Question

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

3x5+4=7
3
x
5
+
4
=
7
Start Fraction 3 x over 5 End Fraction plus 4 equals 7

x2−10=15
x
2
−
10
=
15
x squared minus 10 equals 15

x+x−9=1+x
x
+
x
−
9
=
1
+
x

x plus x minus 9 equals 1 plus x

2x−20=30

Answer 1

To find which equation matches the solution set of {5}, we can solve each of the provided equations for \( x \) and check which one gives the solution \( x = 5 \).

1. **Equation**: \( \frac{3x}{5} + 4 = 7 \)
\[
\frac{3x}{5} = 7 - 4 \\
\frac{3x}{5} = 3 \\
3x = 15 \\
x = 5
\]

2. **Equation**: \( x^2 - 10 = 15 \)
\[
x^2 = 15 + 10 \\
x^2 = 25 \\
x = 5 \quad \text{or} \quad x = -5
\]

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

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

From the above calculations, we see that the first equation \( \frac{3x}{5} + 4 = 7 \) and the second equation \( x^2 - 10 = 15 \) both yield \( x = 5 \). However, since we are looking for one equation that matches the solution set of {5} exactly, we should select:

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