Question

Solve for x in the equation √(x + 9) - 4 = 1. Please select the correct option from the following:

A) x = 16, solution is not extraneous
B) x = 16, solution is extraneous
C) x = 34, solution is not extraneous
D) x = 34, solution is extraneous

Answer 1

To solve for x in the equation √(x + 9) - 4 = 1, add 4 to both sides, square both sides, and subtract 9 from both sides to find x = 16 (option A).

Step-by-step explanation:

To solve for x in the equation √(x + 9) - 4 = 1, we need to isolate the variable x. First, we add 4 to both sides of the equation to get √(x + 9) = 5.

Then, we square both sides of the equation to eliminate the square root: (√(x + 9))^2 = 5^2. This simplifies to x + 9 = 25. Finally, we subtract 9 from both sides to obtain the solution x = 16.

The correct option from the provided choices is A) x = 16, solution is not extraneous.