Which equation matches the solution set of {5}

Question

?(1 point)
Responses

x2−10=15
x squared minus 10 equals 15

x+x−9=1+x
x plus x minus 9 equals 1 plus x

2x−20=30
2 x minus 20 equals 30

3x5+4=7

Answer 1

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

1. Equation 1: \( x^2 - 10 = 15 \)

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

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

   Substitute \( x = 5 \): \[ 5 + 5 - 9 = 1 + 5 \ 1 = 6 \quad \text{(False)} \]

3. Equation 3: \( 2x - 20 = 30 \)

   Substitute \( x = 5 \): \[ 2(5) - 20 = 30 \ 10 - 20 = 30 \ -10 = 30 \quad \text{(False)} \]

4. Equation 4: \( 3x + 4 = 7 \)

   Substitute \( x = 5 \): \[ 3(5) + 4 = 7 \ 15 + 4 = 7 \ 19 = 7 \quad \text{(False)} \]

Only the first equation \( x^2 - 10 = 15 \) holds true when \( x = 5 \). Therefore, the equation that matches the solution set of {5} is:

x^2 - 10 = 15.