Question

Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.

The square root of the quantity 3 x plus 12 end quantity equals 9.

Answer 1

To solve √(3x + 12) = 9, square both sides to get 3x + 12 = 81, simplify to x = 23, and check the solution to confirm it's not extraneous.

Step-by-step explanation:

To solve for x in the given equation where the square root of the quantity 3x plus 12 equals 9, first we need to square both sides of the equation to eliminate the square root, resulting in:

(√(3x + 12))^2 = 9^2

Which simplifies to:

3x + 12 = 81

Subtracting 12 from both sides gives us:

3x = 69

Dividing both sides by 3 results in:

x = 23

Finally, we must check if our solution is extraneous. Substituting x back into the original equation:

√(3(23) + 12) = √(69 + 12)

√81 = 9

This confirms that 9 equals 9, so our solution is not extraneous. The final solution is that x equals 23.