Question

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

2x−20=30
2 x minus 20 equals 30

x2−10=15
x squared minus 10 equals 15

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

x+x−9=1+x

Answer 1

To find which equation matches the solution set of \(\{5\}\), we need to solve each of the equations for \(x\) and see which one has a solution of \(x = 5\).

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

Solve for \(x\):
\[
2x = 30 + 20
\]
\[
2x = 50
\]
\[
x = 25
\]

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

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

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

Solve for \(x\):
\[
\frac{3x}{5} = 7 - 4
\]
\[
\frac{3x}{5} = 3
\]
\[
3x = 15
\]
\[
x = 5
\]

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

Simplify and solve for \(x\):
\[
2x - 9 = 1 + x
\]
\[
2x - x = 1 + 9
\]
\[
x = 10
\]

Now, let's summarize the solutions:

1. \(x = 25\)
2. \(x = 5\) or \(x = -5\)
3. \(x = 5\)
4. \(x = 10\)

The equations that give the solution of \(5\) are the second and third equations. However, since we're looking for the solution set of exactly \(\{5\}\), the second equation also gives another solution \(-5\), so the best match is the third equation.

So, the answer is:

**3x/5 + 4 = 7**.