Asked by cheyanne
                Solve. Check for extraneous solutions.
1) (/3x+7) = x-1
2) (3/2x)-3=9
Note: (/3x+7) is the square root of 3x plus 7 and (3/2x)-3=9 is 3 times the square root of 2x - 3 equals 9.
            
            
        1) (/3x+7) = x-1
2) (3/2x)-3=9
Note: (/3x+7) is the square root of 3x plus 7 and (3/2x)-3=9 is 3 times the square root of 2x - 3 equals 9.
Answers
                    Answered by
            Henry
            
    1. sqrt(3x+7) = x-1.
Square both sides:
3x + 7 = x^2 - 2x + 1.
-x^2 + 2x +3x = 1 - 7 = - 6.
Multiply both sides by -1:
x^2 -2x -3x = 6.
x^2 - 5x - 6 = 0.
(x+1)(x-6) = 0.
x+1 = 0.
X = -1. Does not satisfy original Eq.
x-6 = 0.
X = 6.
2. 3*sqrt(2x) - 3 = 9.
3*sqrt(2x) = 9+3 = 12.
Divide both sides by 3:
sqrt(2x) = 4.
Square both sides:
2x = 16.
X = 8.
    
Square both sides:
3x + 7 = x^2 - 2x + 1.
-x^2 + 2x +3x = 1 - 7 = - 6.
Multiply both sides by -1:
x^2 -2x -3x = 6.
x^2 - 5x - 6 = 0.
(x+1)(x-6) = 0.
x+1 = 0.
X = -1. Does not satisfy original Eq.
x-6 = 0.
X = 6.
2. 3*sqrt(2x) - 3 = 9.
3*sqrt(2x) = 9+3 = 12.
Divide both sides by 3:
sqrt(2x) = 4.
Square both sides:
2x = 16.
X = 8.
                                                    There are no AI answers yet. The ability to request AI answers is coming soon!
                                            
                Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.