Question

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

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

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

2x−20=30
2 x minus 20 equals 30

x2−10=15

Answer 1

To find the equation that matches the solution set of {5}, we need to solve each equation and see which one has 5 as its solution.

1. **3x/5 + 4 = 7**
\[
3x/5 + 4 = 7
\]
Subtract 4 from both sides:
\[
3x/5 = 3
\]
Multiply both sides by 5:
\[
3x = 15
\]
Divide both sides by 3:
\[
x = 5
\]

2. **x + x - 9 = 1 + x**
\[
2x - 9 = 1 + x
\]
Subtract x from both sides:
\[
x - 9 = 1
\]
Add 9 to both sides:
\[
x = 10
\]

3. **2x - 20 = 30**
\[
2x - 20 = 30
\]
Add 20 to both sides:
\[
2x = 50
\]
Divide both sides by 2:
\[
x = 25
\]

4. **x^2 - 10 = 15**
\[
x^2 - 10 = 15
\]
Add 10 to both sides:
\[
x^2 = 25
\]
Take the square root of both sides:
\[
x = 5 \quad \text{or} \quad x = -5
\]

From the calculations, the first equation \(3x/5 + 4 = 7\) has the solution \(x = 5\), and the fourth equation \(x^2 - 10 = 15\) also has \(x = 5\) (along with \(x = -5\)).

Therefore, the equations that match the solution set of {5} are:
- **3x/5 + 4 = 7**
- **x^2 - 10 = 15**

However, if we are looking for only one equation that matches specifically {5}, the best choice is:
- **3x/5 + 4 = 7**.