Question

What is the answer? I can't figure it out.

Answer 1

`√(2z - 6) - √(z + 6) = 0`


`√(2z - 6) = √(z + 6)`


`(√(2z - 6))^2 = (√(z + 6))^2`


`2z - 6 = z + 6`


`z - 6 = 6`


`z = 12`

Since we squared both sides, we must check the solution on the original equation.


`√(2(12) - 6) - √(12 + 6) = 0`


`√(24 - 6) - √(18) = 0`


`√(18) - √(18) = 0`


`0 = 0`

Since the solution makes for a true statement, z = 12 is the solution.

Answer: D. z = 12

Answer 2

rearranging:-)
sqrt(2z - 6) = sqrt(z + 6
squaring both sides
2z - 6 = z + 6
2z - z = 6 + 6
z = 12 (answer)