Question 1100461
 |x-3| = 2x+1
x - 3 = 2x + 1
-3 - 1 = 2x - x
-4 = x, an extraneous solution, as you can see if you substitute in the original equation
|-4 - 3| = 2(-4) + 1
|-7| = -8 + 1
Absolute is always positive
+7  does not = -7
:
Solution 2
|x - 3| = 2x + 1
x - 3 = -(2x + 1)
x - 3 = -2x - 1
x + 2x = -1 + 3
3x = 2
x = 2/3, this solution will work in the original equation
:
|(2/3)-3)| = 2(2/3) + 1
|- 7/3| = +7/3
+7/3 = +7/3