Which of the following values of x makes the equation 2x−−√+13=27

Question

true?(1 point)
Responses

25
25

16
16

49
49

9

Answer 1

To solve the equation \( \sqrt{2x} + 13 = 27 \), we'll isolate \( \sqrt{2x} \) first. Here are the steps:

1. Subtract 13 from both sides: \[ \sqrt{2x} = 27 - 13 \] \[ \sqrt{2x} = 14 \]

2. Square both sides to eliminate the square root: \[ 2x = 14^2 \] \[ 2x = 196 \]

3. Divide both sides by 2 to solve for \( x \): \[ x = \frac{196}{2} \] \[ x = 98 \]

Now, let's check the given responses: 25, 16, 49, and 9. None of these match the calculated value of 98, which means none of the provided values make the equation true.