Question

Which equation matches {5}

2x - 20 = 30
x + x - 9 = 1 + x
x^2 - 10 = 15
3x/5 + 4 = 7

Answer 1

To determine which equation corresponds to the solution \( x = 5 \), we will substitute \( x = 5 \) into each equation and check if they hold true.

1. **Equation: \( 2x - 20 = 30 \)**
\[
2(5) - 20 = 30 \\
10 - 20 = 30 \\
-10 \neq 30 \quad \text{(False)}
\]

2. **Equation: \( x + x - 9 = 1 + x \)**
\[
5 + 5 - 9 = 1 + 5 \\
10 - 9 = 6 \\
1 \neq 6 \quad \text{(False)}
\]

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

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

The equations \( x^2 - 10 = 15 \) and \( \frac{3x}{5} + 4 = 7 \) both satisfy \( x = 5 \). Therefore, the equations that match \( x = 5 \) are:

- **\( x^2 - 10 = 15 \)**
- **\( \frac{3x}{5} + 4 = 7 \)**