Find the Domain |4x-1|-|2x-3|+|x-2|=0

Problem

|4*x−1|−|2*x−3|+|x−2|=0

Solution

1. Identify the nature of the task. The expression is an equation involving absolute values. Finding the domain of an equation typically refers to the set of all real numbers for which the expression is defined.

2. Analyze the components of the equation. The expression consists of three absolute value terms: |4*x−1| |2*x−3| and |x−2|

3. Determine if there are any restrictions. Absolute value functions are defined for all real numbers. There are no denominators that could be zero, no square roots of negative numbers, and no logarithms of non-positive numbers.

4. Conclude that since every term in the equation is defined for any real value of x the domain is the set of all real numbers.

Final Answer

Domain=(−∞,∞)

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