9. solve the equation. check for extraneous solutions. type your answers in the blanks. show your work.
|4x + 3| = 9 + 2x

x = or

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:
and

The second one simplifies to

Now solve each for x:

and x=3
The second one:

and x=-2
If you check both of these solutions, they both work; neither are extraneous.