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

prelimaf1

prelimaf1

Answered question

2021-12-07

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

Answer & Explanation

Lible1953

Lible1953

Beginner2021-12-08Added 16 answers

Step 1
Modulus function is also known as absolute value function. It is represented by |x| where x is any number .
It always gives positive value whatever the value is given to the function.
f(x)={xfor x>0xfor x<0 
Step 2
It is given that m>0 so |2x-3|-m is positive.
So |2x-3|-m=m
|2x-3|-m=m
|2x-3|=2m
2x3=±2m
2x=3±2m
x=3±2m2
Step 3
Also the value of x is calculated by expression |2x−3|=0
|2x-3|=0
2x-3=0
2x=3
x=32
Therefore x=(3+2m)2,(32m)2  and  32 are the solution of equation .
So there are three solutions of the given equation.

2022-08-23

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

 

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