Find the Domain 3-2|0.5x+1.5|=-2

Problem

3−2*|0.5*x+1.5|=−2

Solution

1. Identify the nature of the expression. The given equation is an absolute value equation involving a linear expression within the absolute value bars.

2. Determine the domain of the variable x In any expression of the form ƒ(x)=|a*x+b| the absolute value function is defined for all real numbers.

3. Check for restrictions. There are no denominators containing variables, no square roots of negative numbers, and no logarithmic arguments that would restrict the values x can take.

4. Conclude that since the expression 0.5x + 1.5$ is a polynomial (specifically a linear function), it is defined for all real numbers.

Final Answer

Domain=(−∞,∞)

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