Dear Shreshth

As you have well noticed, when you open the modulus and solve the equation, you get two values: x= 2/3 and x= -4. None of these however satisfy the equation!

I'll explain why this happens.

We can rewrite the given equation as:

|2x+1| = x-3.

I've drawn the graph of y= |2x+1| below.

Attachment:

Mod Ques.PNG [ 9.72 KiB | Viewed 239 times ]
As becomes clear from the graph,

For x>-1/2, |2x+1| = 2x+1

For x< -1/2, |2x+1| = -(2x+1)So, when we open the modulus, we should actually write the equations like this:

For x<-1/2, -(2x+1)= x-3

-2x-x= -3+1

-3x= -2

x= 2/3

However, since this solution falls outside the region x<-1/2 for which the equation is valid, it cannot be accepted.

Similarly,

For x >1/2,2x+1 = x-3

2x-x= -3-1

x= -4

However, since this solution falls outside the region x>1/2, for which the equation is valid, it cannot be accepted.

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