SOLUTION: i am not able to solve this question please help me...... |1-x|=|2x+3|

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Question 927106: i am not able to solve this question please help me......
|1-x|=|2x+3|
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
An equation that looks like this typically
has a solution set of 2 values for +x+
--------------
+abs%28+1+-+x+%29+=+abs%28+2x+%2B+3+%29+
------------------------------
The way to think of this is to simplify it
Suppose you have:
+abs%28+j+%29+=+abs%28+k+%29+
This looks like +j+=+k+, but +j+=+-k+
also works ( definition of absolute value )
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Now go back to your problem and do the same thing
(1) +1+-+x+=+2x+%2B+3+ works, but
(2) +1+-+x+=+-%28+2x+%2B+3+%29+ also works
------------------------------------
Solve:
(1) +1+-+x+=+2x+%2B+3+
(1) +3x+=+-2+
(1) +x+=+-2%2F3+
-------------------
Solve:
(2) +1+-+x+=+-%28+2x+%2B+3+%29+
(2) +1+-+x+=+-2x+-+3+
(2) +x+=+-4+
----------------
The solutions are:
+x+=+-2%2F3+
+x+=+-4+
------------------
check:
+abs%28+1+-+x+%29+=+abs%28+2x+%2B+3+%29+
+abs%28+1+-+%28-2%2F3%29+%29+=+abs%28+2%2A%28-2%2F3%29+%2B+3+%29+
+abs%28+5%2F3+%29+=+abs%28+-4%2F3+%2B+9%2F3+%29+
+abs%28+5%2F3+%29+=+abs%28+5%2F3+%29+
--------------------------
+abs%28+1+-+x+%29+=+abs%28+2x+%2B+3+%29+
+abs%28+1+-+%28-4%29+%29+=+abs%28+2%2A%28-4%29+%2B+3+%29+
+abs%28+5+%29+=+abs%28+-8+%2B+3+%29+
+abs%28+5+%29+=+abs%28+-5+%29+
OK