Question

Which equation matches the solution set of {5}?(1 point)Responses2x−20=302 x minus 20 equals 30x+x−9=1+xx plus x minus 9 equals 1 plus x3x5+4=7Start Fraction 3 x over 5 End Fraction plus 4 equals 7x2−10=15

Answer 1

To find which equation matches the solution set of {5}, we will substitute \( x = 5 \) into each equation and see which one holds true.

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

Substituting \( x = 5 \):
\[
2(5) - 20 = 10 - 20 = -10 \quad \text{(not equal to } 30\text{)}
\]

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

Simplifying:
\[
2x - 9 = 1 + x
\]
Substituting \( x = 5 \):
\[
2(5) - 9 = 1 + 5 \implies 10 - 9 = 6 \implies 1 \neq 6 \quad \text{(not true)}
\]

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

Substituting \( x = 5 \):
\[
\frac{3(5)}{5} + 4 = 7 \implies 3 + 4 = 7 \quad \text{(true)}
\]

4. **Equation**: \( x^2 - 10 = 15 \)

Substituting \( x = 5 \):
\[
5^2 - 10 = 15 \implies 25 - 10 = 15 \quad \text{(true)}
\]

Now let's summarize the results:

- **Equation 1**: \( 2x - 20 = 30 \) **(Not true)**
- **Equation 2**: \( x + x - 9 = 1 + x \) **(Not true)**
- **Equation 3**: \( \frac{3x}{5} + 4 = 7 \) **(True)**
- **Equation 4**: \( x^2 - 10 = 15 \) **(True)**

Thus, the equations that match the solution set of \({5}\) are:

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

However, if the task is to select only one, **the equation that directly results in the solution set {5} is better represented by the more straightforward and linear equation:**

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