Question

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!! I CANNOT RETAKE THIS!!

Which statement best reflects the solution(s) of the equation?

Answer 1

`√(3x + 1) = x - 3\\\\3x + 1 = (x - 3)^2\\\\3x + 1 = x^2 + 9 - 6x\\\\x^2 - 9x + 8 = 0\\\\x = 8\;or\;x = 1`

but x = 1 does not satisfy the Equation

So, The answer is :

There is only one solution : x = 8

The solution x = 1 is an extraneous solution

Answer 2

Answer: x = 8

x = 1 is an extraneous solution

Explanation:

`√(3x+1)` - x + 3 = 0

RESTRICTIONS: 3x + 1 ≥ 0 → x ≥
`-(1)/(3)` (because square roots cannot be less than zero/negative)

`√(3x+1)` - x + 3 = 0

+x -3 +x -3

`√(3x+1)` = x - 3

`(√(3x+1))^(2)` = (x - 3)²

3x + 1 = x² - 6x + 9

-3x -1 -3x -1

0 = x² - 9x + 8

0 = (x - 1)(x - 8)

0 = x - 1 0 = x - 8

+1 +1 +8 +8

1 = x 8 = x both solutions are ≥
`-(1)/(3)`

Check:

x = 1:
`√(3(1)+1)` - (1) + 3 = 0

2 - 1 + 3 = 0

4 = 0

FALSE so x = 1 is NOT a valid solution

x = 8:
`√(3(8)+1)` - (8) + 3 = 0

5 - 8 + 3 = 0

0 = 0

TRUE so x = 8 is a valid solution