how many solutions dose the equation ||2x-3|-m|=m have

Reshama Oti

Reshama Oti

Answered question

2022-08-23

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

Answer & Explanation

xleb123

xleb123

Skilled2023-06-03Added 181 answers

To determine the number of solutions for the equation ||2x3|m|=m when m>0, we can consider different cases based on the absolute value expression.
Let's analyze the equation step by step.
1. When 2x3 is positive or zero (|2x3|0):
In this case, the equation becomes |2x3|m=m. Solving for |2x3|, we have |2x3|=2m. Since m>0, the absolute value of any number is always non-negative. Therefore, |2x3|=2m always has a solution.
2. When 2x3 is negative (|2x3|<0):
In this case, the equation becomes (2x3)m=m. Simplifying, we have 2x+3=2m. Solving for x, we get x=32m2.
Now, let's summarize the cases:
Case 1: When 2x30
- The equation |2x3|m=m always has a solution.
Case 2: When 2x3<0
- The equation |2x3|m=m has a solution x=32m2.
In both cases, we have at least one solution for the equation.
Therefore, the equation ||2x3|m|=m has at least one solution when m>0.

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