SOLUTION: How many solutions are there to the equality | x - |2x + 1|

Click here to see ALL problems on absolute-value

Question 319009: How many solutions are there to the equality | x - |2x + 1| | = 3?

Answer by CharlesG2(834) (Show Source):
You can put this solution on YOUR website!
How many solutions are there to the equality | x - |2x + 1| | = 3?
| x - |2x + 1| | = 3
this is equivalent to
x - |2x + 1| = -3 OR x - |2x + 1| = 3
-|2x + 1| = -3 - x -|2x + 1| = 3 - x
|2x + 1| = x + 3 |2x + 1| = x - 3
|2x + 1| = x + 3
this is equivalent to
2x + 1 = -(x + 3) OR 2x + 1 = x + 3
2x + 1 = -x - 3 x = 2
3x = -4
x = -4/3
2 Solutions
check:
| x - |2x + 1| | = 3 plug in -4/3
| (-4/3) - |2(-4/3) + 1| | = 3
| -4/3 - |-8/3 + 1| | = 3
| -4/3 - |-5/3| | = 3
| -4/3 - 5/3 | = 3
| -9/3 | = 3
9/3 = 3
| x - |2x + 1| | = 3 plug in 2
| (2) - |2(2) + 1| | = 3
| 2 - |4 + 1| | = 3
| 2 - 5 | = 3
| -3 | = 3
3 = 3
2 Solutions

SOLUTION: How many solutions are there to the equality | x - |2x + 1| | = 3?