Determine if Linear 4x(y+11)=5-4y(2-x)

$4 x (y + 11) = 5 - 4 y (2 - x)$

Step 1

Solve the equation for $y$ .

Simplify $4 x (y + 11)$ .

Rewrite.

$0 + 0 + 4 x (y + 11) = 5 - 4 y (2 - x)$

Simplify by adding zeros.

$4 x (y + 11) = 5 - 4 y (2 - x)$

Apply the distributive property.

$4 x y + 4 x \cdot 11 = 5 - 4 y (2 - x)$

Multiply $11$ by $4$ .

$4 x y + 44 x = 5 - 4 y (2 - x)$

Simplify each term.

Apply the distributive property.

$4 x y + 44 x = 5 - 4 y \cdot 2 - 4 y (- x)$

Multiply $2$ by $- 4$ .

$4 x y + 44 x = 5 - 8 y - 4 y (- x)$

Rewrite using the commutative property of multiplication.

$4 x y + 44 x = 5 - 8 y - 4 \cdot - 1 y x$

Multiply $- 4$ by $- 1$ .

$4 x y + 44 x = 5 - 8 y + 4 y x$

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

$5 - 8 y + 4 y x = 4 x y + 44 x$

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

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

$5 - 8 y + 4 y x - 4 x y = 44 x$

Combine the opposite terms in $5 - 8 y + 4 y x - 4 x y$ .

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

$5 - 8 y + 4 x y - 4 x y = 44 x$

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

$5 - 8 y + 0 = 44 x$

Add $5 - 8 y$ and $0$ .

$5 - 8 y = 44 x$

Subtract $5$ from both sides of the equation.

$- 8 y = 44 x - 5$

Divide each term in $- 8 y = 44 x - 5$ by $- 8$ and simplify.

Divide each term in $- 8 y = 44 x - 5$ by $- 8$ .

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

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $44$ and $- 8$ .

Factor $4$ out of $44 x$ .

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

Cancel the common factors.

Factor $4$ out of $- 8$ .

$y = \frac{4 (11 x)}{4 (- 2)} + \frac{- 5}{- 8}$

Cancel the common factor.

$y = \frac{4 (11 x)}{4 \cdot - 2} + \frac{- 5}{- 8}$

Rewrite the expression.

$y = \frac{11 x}{- 2} + \frac{- 5}{- 8}$

Move the negative in front of the fraction.

$y = - \frac{11 x}{2} + \frac{- 5}{- 8}$

Dividing two negative values results in a positive value.

$y = - \frac{11 x}{2} + \frac{5}{8}$

Step 2

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+11)=5-4y(2-x)

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