Determine if Linear 4x(y+8)=5-4y(11-x)

$4 x (y + 8) = 5 - 4 y (11 - x)$

Solve the equation for $y$ .

Simplify $4 x (y + 8)$ .

Rewrite.

$0 + 0 + 4 x (y + 8) = 5 - 4 y (11 - x)$

Simplify by adding zeros.

$4 x (y + 8) = 5 - 4 y (11 - x)$

Apply the distributive property.

$4 x y + 4 x \cdot 8 = 5 - 4 y (11 - x)$

Multiply $8$ by $4$ .

$4 x y + 32 x = 5 - 4 y (11 - x)$

Simplify each term.

Apply the distributive property.

$4 x y + 32 x = 5 - 4 y \cdot 11 - 4 y (- x)$

Multiply $11$ by $- 4$ .

$4 x y + 32 x = 5 - 44 y - 4 y (- x)$

Rewrite using the commutative property of multiplication.

$4 x y + 32 x = 5 - 44 y - 4 \cdot - 1 y x$

Multiply $- 4$ by $- 1$ .

$4 x y + 32 x = 5 - 44 y + 4 y x$

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$5 - 44 y + 4 y x = 4 x y + 32 x$

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

Subtract $4 x y$ from both sides of the equation.

$5 - 44 y + 4 y x - 4 x y = 32 x$

Combine the opposite terms in $5 - 44 y + 4 y x - 4 x y$ .

Reorder the factors in the terms $4 y x$ and $- 4 x y$ .

$5 - 44 y + 4 x y - 4 x y = 32 x$

Subtract $4 x y$ from $4 x y$ .

$5 - 44 y + 0 = 32 x$

Add $5 - 44 y$ and $0$ .

$5 - 44 y = 32 x$

Subtract $5$ from both sides of the equation.

$- 44 y = 32 x - 5$

Divide each term in $- 44 y = 32 x - 5$ by $- 44$ and simplify.

Divide each term in $- 44 y = 32 x - 5$ by $- 44$ .

$\frac{- 44 y}{- 44} = \frac{32 x}{- 44} + \frac{- 5}{- 44}$

Simplify the left side.

Cancel the common factor of $- 44$ .

Cancel the common factor.

$\frac{- 44 y}{- 44} = \frac{32 x}{- 44} + \frac{- 5}{- 44}$

Divide $y$ by $1$ .

$y = \frac{32 x}{- 44} + \frac{- 5}{- 44}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $32$ and $- 44$ .

Factor $4$ out of $32 x$ .

$y = \frac{4 (8 x)}{- 44} + \frac{- 5}{- 44}$

Cancel the common factors.

Factor $4$ out of $- 44$ .

$y = \frac{4 (8 x)}{4 (- 11)} + \frac{- 5}{- 44}$

Cancel the common factor.

$y = \frac{4 (8 x)}{4 \cdot - 11} + \frac{- 5}{- 44}$

Rewrite the expression.

$y = \frac{8 x}{- 11} + \frac{- 5}{- 44}$

Move the negative in front of the fraction.

$y = - \frac{8 x}{11} + \frac{- 5}{- 44}$

Dividing two negative values results in a positive value.

$y = - \frac{8 x}{11} + \frac{5}{44}$

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ and the degree of variable $x$ is $1$ .

Linear

Determine if Linear 4x(y+8)=5-4y(11-x)

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