Determine if Linear 8x(y+3)=11-8y(12-x)

$8 x (y + 3) = 11 - 8 y (12 - x)$

Step 1

Solve the equation for $y$ .

Simplify $8 x (y + 3)$ .

Rewrite.

$0 + 0 + 8 x (y + 3) = 11 - 8 y (12 - x)$

Simplify by adding zeros.

$8 x (y + 3) = 11 - 8 y (12 - x)$

Apply the distributive property.

$8 x y + 8 x \cdot 3 = 11 - 8 y (12 - x)$

Multiply $3$ by $8$ .

$8 x y + 24 x = 11 - 8 y (12 - x)$

Simplify each term.

Apply the distributive property.

$8 x y + 24 x = 11 - 8 y \cdot 12 - 8 y (- x)$

Multiply $12$ by $- 8$ .

$8 x y + 24 x = 11 - 96 y - 8 y (- x)$

Rewrite using the commutative property of multiplication.

$8 x y + 24 x = 11 - 96 y - 8 \cdot - 1 y x$

Multiply $- 8$ by $- 1$ .

$8 x y + 24 x = 11 - 96 y + 8 y x$

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

$11 - 96 y + 8 y x = 8 x y + 24 x$

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

Subtract $8 x y$ from both sides of the equation.

$11 - 96 y + 8 y x - 8 x y = 24 x$

Combine the opposite terms in $11 - 96 y + 8 y x - 8 x y$ .

Reorder the factors in the terms $8 y x$ and $- 8 x y$ .

$11 - 96 y + 8 x y - 8 x y = 24 x$

Subtract $8 x y$ from $8 x y$ .

$11 - 96 y + 0 = 24 x$

Add $11 - 96 y$ and $0$ .

$11 - 96 y = 24 x$

Subtract $11$ from both sides of the equation.

$- 96 y = 24 x - 11$

Divide each term in $- 96 y = 24 x - 11$ by $- 96$ and simplify.

Divide each term in $- 96 y = 24 x - 11$ by $- 96$ .

$\frac{- 96 y}{- 96} = \frac{24 x}{- 96} + \frac{- 11}{- 96}$

Simplify the left side.

Cancel the common factor of $- 96$ .

Cancel the common factor.

$\frac{- 96 y}{- 96} = \frac{24 x}{- 96} + \frac{- 11}{- 96}$

Divide $y$ by $1$ .

$y = \frac{24 x}{- 96} + \frac{- 11}{- 96}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $24$ and $- 96$ .

Factor $24$ out of $24 x$ .

$y = \frac{24 (x)}{- 96} + \frac{- 11}{- 96}$

Cancel the common factors.

Factor $24$ out of $- 96$ .

$y = \frac{24 x}{24 \cdot - 4} + \frac{- 11}{- 96}$

Cancel the common factor.

$y = \frac{24 x}{24 \cdot - 4} + \frac{- 11}{- 96}$

Rewrite the expression.

$y = \frac{x}{- 4} + \frac{- 11}{- 96}$

Move the negative in front of the fraction.

$y = - \frac{x}{4} + \frac{- 11}{- 96}$

Dividing two negative values results in a positive value.

$y = - \frac{x}{4} + \frac{11}{96}$

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 8x(y+3)=11-8y(12-x)

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