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

Question

Responses

x^2−10=15
x squared minus 10 equals 15

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

2x−20=30
2 x minus 20 equals 30

x+x−9=1+x

Answer 1

To find which equation has the solution set {5}, we can solve each equation one by one.

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

   \[ x^2 - 10 = 15 \ x^2 = 15 + 10 \ x^2 = 25 \ x = 5 \quad \text{or} \quad x = -5 \]

   Solution set: {5, -5} (does not match {5})

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

   \[ \frac{3x}{5} = 7 - 4 \ \frac{3x}{5} = 3 \ 3x = 3 \cdot 5 \ 3x = 15 \ x = 5 \]

   Solution set: {5} (matches {5})

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

   \[ 2x = 30 + 20 \ 2x = 50 \ x = 25 \]

   Solution set: {25} (does not match {5})

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

   \[ 2x - 9 = 1 + x \ 2x - x = 1 + 9 \ x = 10 \]

   Solution set: {10} (does not match {5})

After checking each equation, the only one that matches the solution set {5} is:

Response: \( \frac{3x}{5} + 4 = 7 \) (matches {5})