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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