Find the Domain -6x-y=3x-3y

$- 6 x - y = 3 x - 3 y$

Step 1

Move all terms containing $y$ to the left side of the equation.

Add $3 y$ to both sides of the equation.

$- 6 x - y + 3 y = 3 x$

Add $- y$ and $3 y$ .

$- 6 x + 2 y = 3 x$

Step 2

Move all terms not containing $y$ to the right side of the equation.

Add $6 x$ to both sides of the equation.

$2 y = 3 x + 6 x$

Add $3 x$ and $6 x$ .

$2 y = 9 x$

Step 3

Divide each term in $2 y = 9 x$ by $2$ and simplify.

Divide each term in $2 y = 9 x$ by $2$ .

$\frac{2 y}{2} = \frac{9 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{9 x}{2}$

Divide $y$ by $1$ .

$y = \frac{9 x}{2}$

Step 4

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 5

Find the Domain -6x-y=3x-3y

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