Question

Which equation matches the solution set of {5} ?

(1 point)
Responses

x + x - 9 = 1 + x
x + x - 9 = 1 + x

2x - 20 = 30
2x - 20 = 30

x2
- 10 = 15
x squared - 10 = 15

3x5 + 4 = 7

Answer 1

To find the equation that matches the solution set of {5}, we can solve each equation for x and determine which one has 5 as the sole solution.

1. **Equation: x + x - 9 = 1 + x**
Simplifying:
\[
2x - 9 = 1 + x \\
2x - x = 1 + 9 \\
x = 10
\]
Solution: {10}

2. **Equation: 2x - 20 = 30**
Solving for x:
\[
2x = 30 + 20 \\
2x = 50 \\
x = 25
\]
Solution: {25}

3. **Equation: x² - 10 = 15**
Rearranging:
\[
x^2 = 15 + 10 \\
x^2 = 25 \\
x = 5 \quad \text{or} \quad x = -5
\]
Solution: {5, -5}

4. **Equation: 3x + 4 = 7**
Solving for x:
\[
3x = 7 - 4 \\
3x = 3 \\
x = 1
\]
Solution: {1}

Thus, the only equation that matches the solution set of {5} is the third one:

**x² - 10 = 15**