Solve the equation V3x -1 = 3x - 7.
Identify the extraneous solution.
Write your answers as reduced fractions, if necessary
To solve the equation V3x - 1 = 3x - 7, we first need to isolate the square root term:
V3x - 1 = 3x - 7
V3x = 3x - 6 (added 1 to both sides)
3x = (3x - 6)^2 (squared both sides)
3x = 9x^2 - 36x + 36 (expanded the squared term)
Rearranging the terms, we get:
9x^2 - 39x + 36 = 0
Now, we can solve this quadratic equation for x by factorization or using the quadratic formula. After solving, we obtain:
x = 4/3 or x = 3
To check for extraneous solutions, we substitute these values back into the original equation:
For x = 4/3:
V3(4/3) - 1 = 3(4/3) - 7
2 - 1 = 4 - 7
1 = -3 (which is false)
Therefore, x = 4/3 is an extraneous solution.
The correct solution to the equation V3x - 1 = 3x - 7 is x = 3.