Question

Which equation matches the solution set of {5} ?(1 point) Responses x+x−9=1+x x plus x minus 9 equals 1 plus x x2−10=15 x squared minus 10 equals 15 3x5+4=7 Start Fraction 3 x over 5 End Fraction plus 4 equals 7 2x−20=30

Answer 1

To determine which equation matches the solution set of \(\{5\}\), we'll solve each equation one by one to see which one yields \(x = 5\).

1. **Equation:** \(x + x - 9 = 1 + x\)
\[
2x - 9 = 1 + x \implies 2x - x = 1 + 9 \implies x = 10
\]

2. **Equation:** \(x^2 - 10 = 15\)
\[
x^2 = 25 \implies x = 5 \text{ or } x = -5
\]

3. **Equation:** \(\frac{3x}{5} + 4 = 7\)
\[
\frac{3x}{5} = 3 \implies 3x = 15 \implies x = 5
\]

4. **Equation:** \(2x - 20 = 30\)
\[
2x = 50 \implies x = 25
\]

From the equations solved, the ones that yield the solution \(x = 5\) are:
- \(x^2 - 10 = 15\) (solution set is \(\{5, -5\}\))
- \(\frac{3x}{5} + 4 = 7\) (solution set is \(\{5\}\))

Thus, the equation that matches the solution set of \(\{5\}\) specifically is:
\[
\frac{3x}{5} + 4 = 7
\]