Find the Domain -2(4x+3)=3(3y+4)

Problem

−2*(4*x+3)=3*(3*y+4)

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. Distribute the constants on both sides of the equation.

−8*x−6=9*y+12

4. Isolate the term containing y by subtracting 12 from both sides.

−8*x−18=9*y

5. Divide by 9 to express y as a function of x

y=(−8*x−18)/9

6. Analyze the resulting function y=−8/9*x−2 Since this is a linear function, there are no values of x that result in division by zero or the square root of a negative number.

7. Conclude that the domain is the set of all real numbers.

Final Answer

Domain: *(−∞,∞)

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