Question

PLEASE HELP!!! 9. Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work.
|4x + 3| = 9 + 2x

x = _____ or _____

Answer 1

x=-2 or x=3 are the answers, hope this helps. 

Answer 2

When you have the absolute value of an equation, in order to remove the absolute value signs, you have to set what's inside the signs equal to both the positive and negative of what the solution set is.  By that I mean:
$4x+3=9+2x$ and
$4x+3=-(9+2x)$
The second one simplifies to
$4x+3=-9-2x$
Now solve each for x:
$4x+3=9+2x$
$2x=6$ and x=3
The second one:
$4x+3=-9-2x$
$6x=-12$ and x=-2
If you check both of these solutions, they both work; neither are extraneous.