What is the solution of the equation? Eliminate any extraneous solutions.
\(\sqrt{3x+28} - 8 = x\)
A. 9 and -4
B. -9
C. -9 and -4
D. -4
Answer (2)
3 x + 28 − 8 = x A . x = 9 ∨ x = − 4 x = 9 → L = 3 ⋅ 9 + 28 − 8 = 27 + 28 − 8 = 55 − 8 R = 9 ; L = R B . x = − 9 L = 3 ⋅ ( − 9 ) + 28 − 8 = − 27 + 28 − 8 = 1 − 8 = 1 − 8 = − 7 ; R = − 9 ; L = R
C . x = − 9 ∨ x = − 4 ( see B . ) D . x = − 4 L = 3 ⋅ ( − 4 ) + 28 − 8 = − 12 + 28 − 8 = 16 − 8 = 4 − 8 = − 4 R = − 4 L = R A n s w er : D .
The solutions to the equation 3 x + 28 − 8 = x are x = − 4 and x = − 9 . After checking, both solutions are valid and no extraneous solutions were found. The answer that fits this is C: -9 and -4.
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