Find the Domain -4x-5y=-6x+5y

$- 4 x - 5 y = - 6 x + 5 y$

Step 1

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

Subtract $5 y$ from both sides of the equation.

$- 4 x - 5 y - 5 y = - 6 x$

Subtract $5 y$ from $- 5 y$ .

$- 4 x - 10 y = - 6 x$

Step 2

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

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

$- 10 y = - 6 x + 4 x$

Add $- 6 x$ and $4 x$ .

$- 10 y = - 2 x$

Step 3

Divide each term in $- 10 y = - 2 x$ by $- 10$ and simplify.

Divide each term in $- 10 y = - 2 x$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{- 2 x}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{- 2 x}{- 10}$

Divide $y$ by $1$ .

$y = \frac{- 2 x}{- 10}$

Simplify the right side.

Cancel the common factor of $- 2$ and $- 10$ .

Factor $- 2$ out of $- 2 x$ .

$y = \frac{- 2 (x)}{- 10}$

Cancel the common factors.

Factor $- 2$ out of $- 10$ .

$y = \frac{- 2 (x)}{- 2 (5)}$

Cancel the common factor.

$y = \frac{- 2 x}{- 2 \cdot 5}$

Rewrite the expression.

$y = \frac{x}{5}$

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 -4x-5y=-6x+5y

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