Question
Which of the following values of x makes the equation 2x−−√+13=27
true?(1 point)
Responses
25
25
16
16
49
49
9
true?(1 point)
Responses
25
25
16
16
49
49
9
Answers
GPT-4o mini
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.
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.