Which equation matches the solution set of {5}

Question

{
5
}
?(1 point)
Responses

x+x−9=1+x
𝑥
+
𝑥
−
9
=
1
+
𝑥

x plus x minus 9 equals 1 plus x

2x−20=30
2
𝑥
−
20
=
30

2 x minus 20 equals 30

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

x2−10=15

Answer 1

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

1. Equation: \( x + x - 9 = 1 + x \)
   Substituting \( x = 5 \): \[ 5 + 5 - 9 = 1 + 5 \ 10 - 9 = 6 \ 1 = 6 , \text{(false)} \]

2. Equation: \( 2x - 20 = 30 \)
   Substituting \( x = 5 \): \[ 2(5) - 20 = 30 \ 10 - 20 = 30 \ -10 = 30 , \text{(false)} \]

3. Equation: \( \frac{3x}{5} + 4 = 7 \)
   Substituting \( x = 5 \): \[ \frac{3(5)}{5} + 4 = 7 \ 3 + 4 = 7 \ 7 = 7 , \text{(true)} \]

4. Equation: \( x^2 - 10 = 15 \)
   Substituting \( x = 5 \): \[ 5^2 - 10 = 15 \ 25 - 10 = 15 \ 15 = 15 , \text{(true)} \]

The equations \( \frac{3x}{5} + 4 = 7 \) and \( x^2 - 10 = 15 \) both yield the solution \( x = 5 \). However, since you are asking for one equation, you can note that both equations provide valid solutions, but if you have to pick one, it might be best to confirm your requirement or specification.

In conclusion, both:

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

are correct answers but if only one is needed, you can choose either of them based on your preference.

Answer 2

pick one

Answer 3

If I have to pick one equation that matches the solution set of \({5}\), I would choose:

\[ \frac{3x}{5} + 4 = 7 \]

This equation is valid as it simplifies correctly to yield the solution \(x = 5\).