Find the Domain 3x-2y=-16

Problem

3*x−2*y=−16

Solution

1. Identify the type of equation. The given equation 3*x−2*y=−16 is a linear equation in two variables.

2. Solve for y to express the equation as a function of x

−2*y=−3*x−16

y=3/2*x+8

3. Analyze the resulting function. The expression 3/2*x+8 is a polynomial (specifically, a linear function).

4. Determine the constraints. Polynomials are defined for all real numbers because there are no denominators containing x that could be zero and no even roots of negative numbers.

5. State the domain in interval notation. Since x can be any real number, the domain is all real numbers.

Final Answer

Domain: *(−∞,∞)

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