Question

What is the solution to the equation 3\sqrt{x-4}-3\sqrt{2x+8}=0 m = –24
m = –12
m = –6
m = –4

Answer 1

Solve 3√(x−4) − 3√(2x+8) = 0:

Divide by 3: √(x−4) = √(2x+8).
Square both sides: x − 4 = 2x + 8 ⇒ x = −12.

Check domain: √(x−4) requires x ≥ 4, and √(2x+8) requires x ≥ −4. The intersection is x ≥ 4, so x = −12 is not allowed (extraneous). Therefore there is no real solution.

(So none of the listed values is a valid solution.)