Question

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

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

x2−10=15
x squared minus 10 equals 15

x+x−9=1+x

Answer 1

To determine which equation has the solution set of \({5}\), we'll solve each equation and see which one results in \(x = 5\).

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

\[
\frac{3x}{5} + 4 = 7
\]
Subtracting 4 from both sides:
\[
\frac{3x}{5} = 3
\]
Multiplying both sides by 5:
\[
3x = 15
\]
Dividing both sides by 3:
\[
x = 5
\]

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

\[
2x - 20 = 30
\]
Adding 20 to both sides:
\[
2x = 50
\]
Dividing both sides by 2:
\[
x = 25
\]

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

\[
x^2 - 10 = 15
\]
Adding 10 to both sides:
\[
x^2 = 25
\]
Taking the square root:
\[
x = 5 \quad \text{or} \quad x = -5
\]

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

\[
2x - 9 = 1 + x
\]
Subtracting \(x\) from both sides:
\[
x - 9 = 1
\]
Adding 9 to both sides:
\[
x = 10
\]

Now, let's summarize the solutions:
- For \( \frac{3x}{5} + 4 = 7 \), we found \( x = 5 \).
- For \( 2x - 20 = 30 \), we found \( x = 25 \).
- For \( x^2 - 10 = 15 \), \( x = 5 \) or \( x = -5 \).
- For \( x + x - 9 = 1 + x \), we found \( x = 10 \).

The equations that yield a solution of \( x = 5 \) are:

1. **\( \frac{3x}{5} + 4 = 7 \)**
2. **\( x^2 - 10 = 15 \)** (since it also has \( x = -5 \))

So, the correct responses that match the solution set of \({5}\) are:
- \( \frac{3x}{5} + 4 = 7 \)
- \( x^2 - 10 = 15 \)

If you're looking for just one equation, it could be either of the above.