Question

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

3x5+4=7
Start Fraction 3 x over 5 End Fraction plus 4 equals 7

2x−20=30
2 x minus 20 equals 30

x2−10=15
x squared minus 10 equals 15

x+x−9=1+x

Answer 1

To find which equation matches the solution set of {5}, we will solve each equation for \( x \) and see if it results in \( x = 5 \).

1. **\( 3x/5 + 4 = 7 \)**

\[
\frac{3x}{5} + 4 = 7
\]
Subtract 4 from both sides:
\[
\frac{3x}{5} = 3
\]
Multiply both sides by 5:
\[
3x = 15
\]
Divide by 3:
\[
x = 5
\]

2. **\( 2x - 20 = 30 \)**

\[
2x - 20 = 30
\]
Add 20 to both sides:
\[
2x = 50
\]
Divide by 2:
\[
x = 25
\]

3. **\( x^2 - 10 = 15 \)**

\[
x^2 - 10 = 15
\]
Add 10 to both sides:
\[
x^2 = 25
\]
Take the square root of both sides:
\[
x = 5 \quad \text{or} \quad x = -5
\]
(However, we are only interested in \( x = 5 \).)

4. **\( x + x - 9 = 1 + x \)**

\[
2x - 9 = 1 + x
\]
Subtract \( x \) from both sides:
\[
x - 9 = 1
\]
Add 9 to both sides:
\[
x = 10
\]

The equations that resulted in a solution of \( x = 5 \) are:

- \( 3x/5 + 4 = 7 \)
- \( x^2 - 10 = 15 \)

Among the options given, both of these equations match the solution set of {5}. However, if you must choose only one from the provided list, it can be the first one:

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