Which equation matches the solution set of {5}

Question

?(1 point)
Responses

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

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

Answer 1

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

1. \( 3x + 4 = 7 \): \[ 3(5) + 4 = 15 + 4 = 19 \quad \text{(not equal to 7)} \]

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

3. \( x + x - 9 = 1 + x \): \[ 5 + 5 - 9 = 1 + 5 \] \[ 10 - 9 = 6 \quad \Rightarrow \quad 1 + 5 = 6 \quad \text{(true)} \]

4. \( 2x - 20 = 30 \): \[ 2(5) - 20 = 30 \quad \Rightarrow \quad 10 - 20 = 30 \] \[ -10 \neq 30 \quad \text{(not true)} \]

From the calculations, two equations hold true when \( x = 5 \):

• \( x^2 - 10 = 15 \)
• \( x + x - 9 = 1 + x \)

However, the question asks for an equation whose solution set is specifically {5}. Only one fits:

The equation \( x^2 - 10 = 15 \) matches the solution set of {5}.