Question

What is the solution of the equation?  Eliminate any extraneous solutions.

√3x+28-8=x

 A. 9 and -4


 B. -9  
C. -9 and -4  
D. -4

Answer 1

`√(3x+28)-8=x\\\\\\A.\ x=9\ \vee\ x=-4\\x=9\to L=√(3\cdot9+28)-8=√(27+28)-8=√(55)-8\\ R=9;\\L\\eq R\\\\B.\ x=-9\\L=√(3\cdot(-9)+28)-8=√(-27+28)-8=\sqrt1-8=1-8=-7;\\ R=-9;\ L\\eq R`


`C.\ x=-9\ \vee\ x=-4\ (see\ B.)\\\\D.\ x=-4\\L=√(3\cdot(-4)+28)-8=√(-12+28)-8=√(16)-8\\=4-8=-4\\R=-4\\L=R\\\\Answer:D.`