Find the Domain 2x-2y=5x-4y

$2 x - 2 y = 5 x - 4 y$

Step 1

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

Add $4 y$ to both sides of the equation.

$2 x - 2 y + 4 y = 5 x$

Add $- 2 y$ and $4 y$ .

$2 x + 2 y = 5 x$

Step 2

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

Subtract $2 x$ from both sides of the equation.

$2 y = 5 x - 2 x$

Subtract $2 x$ from $5 x$ .

$2 y = 3 x$

Step 3

Divide each term in $2 y = 3 x$ by $2$ and simplify.

Divide each term in $2 y = 3 x$ by $2$ .

$\frac{2 y}{2} = \frac{3 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{3 x}{2}$

Divide $y$ by $1$ .

$y = \frac{3 x}{2}$

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 2x-2y=5x-4y

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