Solve for x in the equation: 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: x^2 - 9x + 8 = 0 => (x - 8)(x - 1) = 0. Step 3. Test candidate x = 1: sqrt(4) = 2, but 1 - 3 = -2 (extraneous). Step 4. Test candidate x = 8: sqrt(25) = 5 and 8 - 3 = 5 (valid). Thus x = 8 is the unique solution. Answer: x = 8. Why not the others: x = 1 is an extraneous root generated by squaring both sides; including both is incorrect.
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