Question

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

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

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

2x−20=30
2 x minus 20 equals 30

x+x−9=1+x

Answer 1

To find which equation has the solution set {5}, we can solve each equation one by one.

1. **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 set: {5, -5} (does not match {5})

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

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

Solution set: {5} (matches {5})

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

\[
2x = 30 + 20 \\
2x = 50 \\
x = 25
\]

Solution set: {25} (does not match {5})

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

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

Solution set: {10} (does not match {5})

After checking each equation, the only one that matches the solution set {5} is:

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