Question

Solve |7x +42| = 14x. Identify the solution and an extraneous solution.
A. Solution: x = -2;
extraneous solution: x = 6
B. Solution: x = 6;
extraneous solution: a = -6
C. Solution: x = 6;
extraneous solution: x = -2
D. Solution: x = = 2;
extraneous solution: a = -6

Answer 1

First Case

$|7x+42|=14x\\\\7x+42=14x\\\\42=7x\\\\6=x$

Second case

$-|7x+42|=14x\\\\-7x-42=14x\\\\-42=21x\\\\-2=x$

Verify into first case

$|7(6)+42|=14(6)\\\\|84|=84\\\\84=84\\\\LS=RS$

$|7(-2)+42|=14(-2)\\\\28\neq -28\\\\LS\neq RS$

The solution is 6 and the extraneous solution is -2, which makes the answer C.