Find the Domain (-2x+6y)/3=4

$\frac{- 2 x + 6 y}{3} = 4$

Step 1

Multiply both sides by $3$ .

$\frac{- 2 x + 6 y}{3} \cdot 3 = 4 \cdot 3$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{- 2 x + 6 y}{3} \cdot 3$ .

Factor $2$ out of $- 2 x + 6 y$ .

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

$\frac{2 (- x) + 6 y}{3} \cdot 3 = 4 \cdot 3$

Factor $2$ out of $6 y$ .

$\frac{2 (- x) + 2 (3 y)}{3} \cdot 3 = 4 \cdot 3$

Factor $2$ out of $2 (- x) + 2 (3 y)$ .

$\frac{2 (- x + 3 y)}{3} \cdot 3 = 4 \cdot 3$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2 (- x + 3 y)}{3} \cdot 3 = 4 \cdot 3$

Rewrite the expression.

$2 (- x + 3 y) = 4 \cdot 3$

Apply the distributive property.

$2 (- x) + 2 (3 y) = 4 \cdot 3$

Multiply.

Multiply $- 1$ by $2$ .

$- 2 x + 2 (3 y) = 4 \cdot 3$

Multiply $3$ by $2$ .

$- 2 x + 6 y = 4 \cdot 3$

Simplify the right side.

Multiply $4$ by $3$ .

$- 2 x + 6 y = 12$

Step 3

Solve for $y$ .

Add $2 x$ to both sides of the equation.

$6 y = 12 + 2 x$

Divide each term in $6 y = 12 + 2 x$ by $6$ and simplify.

Divide each term in $6 y = 12 + 2 x$ by $6$ .

$\frac{6 y}{6} = \frac{12}{6} + \frac{2 x}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{12}{6} + \frac{2 x}{6}$

Divide $y$ by $1$ .

$y = \frac{12}{6} + \frac{2 x}{6}$

Simplify the right side.

Simplify each term.

Divide $12$ by $6$ .

$y = 2 + \frac{2 x}{6}$

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2 x$ .

$y = 2 + \frac{2 (x)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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+6y)/3=4

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