d Problem: How many solutions does the equation \[ ||2x-3|-m|=m \] have  if m>0 ? | Job Exam Rare Mathematics (JEMrare) - Solved MCQs
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Problem: How many solutions does the equation \[ ||2x-3|-m|=m \] have  if m>0 ?

Problem: How many solutions does the equation \[ ||2x-3|-m|=m \] have  if m>0 ?

Solution: 

It is given that ‘m’ is positive, so the LHS of the equation is positive !

Hence we can write,

\[ |2x-3|-m=m \]

or

\[ |2x-3|=2m \]

or

\[ 2x-3=\pm2m \]

or

\[ 2x=(\pm 2m+3) \]

or

\[ x=\frac{\pm2m+3}{2} \]

Which expresses two solutions so for !

But

\[ |2x-3|=0 \]

as well,

So,

from there we can say,

\[ x=\frac{3}{2} \]

is the thired solution,

So the equation has three solutions !

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