Find the Domain -1/3y+4x=3

Problem

−1/3*y+4*x=3

Solution

1. Identify the type of equation. This is a linear equation in two variables, x and y

2. Solve for y in terms of x to determine if there are any restrictions on the input variable x

3. Isolate the y term by subtracting 4*x from both sides of the equation.

−1/3*y=−4*x+3

4. Multiply both sides by −3 to solve for y

y=−3*(−4*x+3)

5. Distribute the constant to simplify the expression.

y=12*x−9

6. Analyze the resulting function. Since y=12*x−9 is a polynomial (specifically a linear function), there are no values of x that would result in division by zero or the square root of a negative number.

7. Conclude that the domain consists of all real numbers.

Final Answer

Domain: *(−∞,∞)

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