Solve and check for extraneous solutions.
[tex] \sqrt{3x+1} = x-1 [/tex]
Answer (2)
D : 3 x + 1 ≥ 0 ∧ x − 1 ≥ 0 D : 3 x ≥ − 1 ∧ x ≥ 1 D : x ≥ − 3 1 ∧ x ≥ 1 D : x ≥ 1 3 x + 1 = x − 1 3 x + 1 = ( x − 1 ) 2 3 x + 1 = x 2 − 2 x + 1 x 2 − 5 x = 0 x ( x − 5 ) = 0 x = 0 ∨ x = 5
The solution is 5. The extraneous solution is 0.
The only solution to the equation 3 x + 1 = x − 1 is x = 5 , while x = 0 is identified as an extraneous solution. By checking both values in the original equation, we confirmed their validity. Therefore, the final solution is x = 5 .
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