Consider the equation 2z−2−−−−−√=5 . Which of the following values for z makes the equation true: 11.5, 12.5, or 13.5?(1 point)

Question

The value of z that makes the equation true is .

Answer 1

To solve the equation \( \sqrt{2z - 2} = 5 \), we will first square both sides:

\[ (\sqrt{2z - 2})^2 = 5^2 \]

This simplifies to:

\[ 2z - 2 = 25 \]

Next, we add 2 to both sides:

\[ 2z = 25 + 2 \] \[ 2z = 27 \]

Now, we divide by 2:

\[ z = \frac{27}{2} = 13.5 \]

Thus, the value of \( z \) that makes the equation true is \( \boxed{13.5} \).