Find the Domain |4x+1|=|3x-5|

Problem

|4*x+1|=|3*x−5|

Solution

1. Identify the nature of the expression. The given equation |4*x+1|=|3*x−5| is an absolute value equation.

2. Determine the domain requirements. The domain of an equation refers to the set of all possible real values for x for which the expressions on both sides are defined.

3. Analyze the functions involved. Both ƒ(x)=|4*x+1| and g(x)=|3*x−5| are absolute value functions of linear polynomials.

4. Evaluate for restrictions. Linear polynomials are defined for all real numbers, and the absolute value function is defined for all real inputs. There are no denominators, square roots of negative numbers, or logarithms to restrict the values of x

5. Conclude that x can be any real number.

Final Answer

Domain: *(−∞,∞)

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