Question

Which equation matches the solution set of {5}
x+x-9=1+x
2x-20=30
x^2-10+15
3x/5+4=7

Answer 1

To determine which of the equations has the solution set of \(\{5\}\), we need to solve each equation and check if \(x = 5\) is a solution.

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

Simplifying,
\[
2x - 9 = 1 + x
\]
Subtract \(x\) from both sides:
\[
x - 9 = 1
\]
Add \(9\) to both sides:
\[
x = 10
\]

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

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

3. **Equation:** \(x^2 - 10 + 15 = 0\)

This can be simplified to:
\[
x^2 + 5 = 0
\]
This does not have real solutions, since \(x^2 = -5\) leads to imaginary solutions.

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

Subtract \(4\) from both sides:
\[
\frac{3x}{5} = 3
\]
Multiplying both sides by \(5\):
\[
3x = 15
\]
Dividing by \(3\):
\[
x = 5
\]

The only equation that has the solution \(x = 5\) is the last one, \(\frac{3x}{5} + 4 = 7\).

Thus, the answer is:

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