Solve for x: sqrt(3x + 1) = x - 3.
Answer and explanation
Correct answer: D. x = 8
- Step 1: Square both sides: 3x + 1 = (x - 3)^2 = x^2 - 6x + 9.
- Step 2: Rearrange to standard form: x^2 - 9x + 8 = 0.
- Step 3: Factor: (x - 8)(x - 1) = 0, giving potential solutions x = 8 and x = 1.
- Step 4: Check extraneous roots: for x = 1, sqrt(4) = 2, but 1 - 3 = -2 (extraneous).
- Step 5: For x = 8, sqrt(25) = 5, and 8 - 3 = 5 (valid). Solution is x = 8.
Answer
x = 8.
Why not the others: 'x = 1' is extraneous because the principal square root cannot equal a negative number; 'x = 8 and x = 1' fails to verify against the original radical; 'x = 5' is an arithmetic error.
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