Consider the equation 2z−2−−−−−√=5

Question

. Which of the following values for z makes the equation true: 11.5, 12.5, or 13.5?(1 point)
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 to eliminate the square root.

1. Squaring both sides: \[ 2z - 2 = 5^2 \] \[ 2z - 2 = 25 \]

2. Next, we add 2 to both sides: \[ 2z = 25 + 2 \] \[ 2z = 27 \]

3. Now, we divide both sides by 2: \[ z = \frac{27}{2} = 13.5 \]

Now we can check the options provided: 11.5, 12.5, and 13.5.

Since we found \( z = 13.5 \), the value of \( z \) that makes the equation true is: \[ \boxed{13.5} \]