Question

Solve: |x+1|=|2x+1|

Answer 1

0, -2/3

Answer 2

-2/3 and 0

Answer 3

To solve this problem and other problems like it, you have to check for break points, points where the different parts of the equations equals zero.

In this case the break points for the equation, |x+1|=|2x+1|, are: For the left part of the equation x=-1 and for the right part x=-1/2.

Then you have to check the three individual cases:

Case I: x<-1
This is when x-values are less than -1, which means that we have to take in consideration what happens to the absolute values in the equation at < -1.
If we insert a value < -1, say -2, to the left part of the equation we see that that part is going to be negative (-2+1 =-1 so it's negative). In that case we have to put a negative sign infront of that part of the equation, since values inside |absolute value signs| can't end up negative.

We get: -(x+1) for the left part and -(2x+1) for the right side giving us:

-(x+1) = -(2x+1) which gives us that x=0

Case II: \[-1\le x < -1/2\]
Now we study the second case where we try values between -1 and -1/2
Just follow the same thought pattern as above and you will get there. Here is what we get:

(x+1) = -(2x+1) which gives us that x=-2/3

Case III: \[x \ge -1/2\]

(x+1)=(2x+1), gives us that x=0

We now have that x=-2/3 and x=0.

Hope this helps!

//Ali