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)
The value of z that makes the equation true is ___

1 answer

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

\[ 2z - 2 = 25 \]

Next, add 2 to both sides:

\[ 2z = 27 \]

Then, divide both sides by 2:

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

Now, we can check if \( z = 13.5 \) makes the original equation true:

\[ \sqrt{2(13.5) - 2} = \sqrt{27 - 2} = \sqrt{25} = 5 \]

This confirms that the equation holds true.

Therefore, the value of \( z \) that makes the equation true is 13.5.