Question

how many solutions does the equation ||2x-3|-m|=m have if m>0?

Answer 1

We have to find the number of solutions of the equation ||2x - 3| - m| = m where m > 0.

solution : here m > 0 , it means ||2x - 3| - m| is positive term.

so, |2x - 3| - m = m

⇒|2x - 3| = 2m

⇒2x - 3 = ± 2m

⇒2x = 3 ± 2m

⇒x = (3 ± 2m)/2

also |2x - 3| = 0 ⇒2x = 3 ⇒x = 3/2

Therefore x = (3 + 2m)/2, (3 - 2m)/2 and 3/2 are the solutions of equation.

so there are three solutions of the given equation.

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Answer 2

Answer:

There will be three solution.

Step-by-step explanation:

|2x-3|-m=m

|2x-3|=m+m

2x-3=|2m|

2x-3=2m               or                              2x-3=-2m

x=(2m+3)/2            or                               x= -(2m+3)/2

and

2x-3=0

x=3/2

so, there is 3 solutions