Question

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

x+x−9=1+x
x plus x minus 9 is equal to 1 plus x

3x5+4=7
3 x over 5 plus 4 is equal to 7

x2+10=15
x squared plus 10 is equal to 15

2x−20=30

Answer 1

To determine which equation matches the solution set of {5}, we will solve each equation for \(x\).

1. **Equation:** \(x + x - 9 = 1 + x\)
- Simplifying: \(2x - 9 = 1 + x\)
- Rearranging: \(2x - x = 1 + 9\)
- So, \(x = 10\) (does not match {5}).

2. **Equation:** \( \frac{3x}{5} + 4 = 7\)
- Simplifying: \( \frac{3x}{5} = 7 - 4\)
- So, \( \frac{3x}{5} = 3\)
- Multiplying both sides by 5: \(3x = 15\)
- Dividing by 3: \(x = 5\) (matches {5}).

3. **Equation:** \(x^2 + 10 = 15\)
- Simplifying: \(x^2 = 15 - 10\)
- So, \(x^2 = 5\)
- Taking the square root: \(x = \sqrt{5}\) or \(x = -\sqrt{5}\) (does not match {5}).

4. **Equation:** \(2x - 20 = 30\)
- Simplifying: \(2x = 30 + 20\)
- So, \(2x = 50\)
- Dividing by 2: \(x = 25\) (does not match {5}).

The only equation that matches the solution set of \{5\} is:

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