How many solutions does the equation ||2x - 3| - m|=m have if m > 0? 1; 2; 3; 4

Mahak Diwakar

Mahak Diwakar

Answered question

2022-08-23

Answer & Explanation

nick1337

nick1337

Expert2023-05-28Added 777 answers

To find the number of solutions for the equation |2x3|m=m, where m>0, we can consider the different cases based on the absolute value expression.
Case 1: 2x30
In this case, the absolute value becomes 2x3, and the equation becomes:
2x3m=m
Simplifying this equation, we get:
2x=4m+3
Dividing both sides by 2, we have:
x=2m+32
Case 2: 2x3<0
In this case, the absolute value becomes (2x3), and the equation becomes:
(2x3)m=m
Simplifying this equation, we get:
2x+3m=m
Bringing like terms to one side, we have:
2x=2m3
Dividing both sides by -2, we get:
x=m+32
So, for each case, we have found a solution for x in terms of m.
Therefore, there are 2 solutions for the equation |2x3|m=m when m>0.
The answer is represented as:
B. 2

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