Finite Math Examples

$7 x (y + 9) = 11 - 7 y (6 - x)$

Step 1

Solve the equation for $y$ .

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Step 1.1

Simplify $7 x (y + 9)$ .

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Step 1.1.1

Rewrite.

$0 + 0 + 7 x (y + 9) = 11 - 7 y (6 - x)$

Step 1.1.2

Simplify by adding zeros.

$7 x (y + 9) = 11 - 7 y (6 - x)$

Step 1.1.3

Apply the distributive property.

$7 x y + 7 x \cdot 9 = 11 - 7 y (6 - x)$

Step 1.1.4

Multiply $9$ by $7$ .

$7 x y + 63 x = 11 - 7 y (6 - x)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$7 x y + 63 x = 11 - 7 y \cdot 6 - 7 y (- x)$

Step 1.2.2

Multiply $6$ by $- 7$ .

$7 x y + 63 x = 11 - 42 y - 7 y (- x)$

Step 1.2.3

Rewrite using the commutative property of multiplication.

$7 x y + 63 x = 11 - 42 y - 7 \cdot - 1 y x$

Step 1.2.4

Multiply $- 7$ by $- 1$ .

$7 x y + 63 x = 11 - 42 y + 7 y x$

Step 1.3

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

$11 - 42 y + 7 y x = 7 x y + 63 x$

Step 1.4

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

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Step 1.4.1

Subtract $7 x y$ from both sides of the equation.

$11 - 42 y + 7 y x - 7 x y = 63 x$

Step 1.4.2

Combine the opposite terms in $11 - 42 y + 7 y x - 7 x y$ .

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Step 1.4.2.1

Reorder the factors in the terms $7 y x$ and $- 7 x y$ .

$11 - 42 y + 7 x y - 7 x y = 63 x$

Step 1.4.2.2

Subtract $7 x y$ from $7 x y$ .

$11 - 42 y + 0 = 63 x$

Step 1.4.2.3

Add $11 - 42 y$ and $0$ .

$11 - 42 y = 63 x$

Step 1.5

Subtract $11$ from both sides of the equation.

$- 42 y = 63 x - 11$

Step 1.6

Divide each term in $- 42 y = 63 x - 11$ by $- 42$ and simplify.

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Step 1.6.1

Divide each term in $- 42 y = 63 x - 11$ by $- 42$ .

$\frac{- 42 y}{- 42} = \frac{63 x}{- 42} + \frac{- 11}{- 42}$

Step 1.6.2

Simplify the left side.

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Step 1.6.2.1

Cancel the common factor of $- 42$ .

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Step 1.6.2.1.1

Cancel the common factor.

$\frac{- 42 y}{- 42} = \frac{63 x}{- 42} + \frac{- 11}{- 42}$

Step 1.6.2.1.2

Divide $y$ by $1$ .

$y = \frac{63 x}{- 42} + \frac{- 11}{- 42}$

Step 1.6.3

Simplify the right side.

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Step 1.6.3.1

Simplify each term.

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Step 1.6.3.1.1

Cancel the common factor of $63$ and $- 42$ .

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Step 1.6.3.1.1.1

Factor $21$ out of $63 x$ .

$y = \frac{21 (3 x)}{- 42} + \frac{- 11}{- 42}$

Step 1.6.3.1.1.2

Cancel the common factors.

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Step 1.6.3.1.1.2.1

Factor $21$ out of $- 42$ .

$y = \frac{21 (3 x)}{21 (- 2)} + \frac{- 11}{- 42}$

Step 1.6.3.1.1.2.2

Cancel the common factor.

$y = \frac{21 (3 x)}{21 \cdot - 2} + \frac{- 11}{- 42}$

Step 1.6.3.1.1.2.3

Rewrite the expression.

$y = \frac{3 x}{- 2} + \frac{- 11}{- 42}$

Step 1.6.3.1.2

Move the negative in front of the fraction.

$y = - \frac{3 x}{2} + \frac{- 11}{- 42}$

Step 1.6.3.1.3

Dividing two negative values results in a positive value.

$y = - \frac{3 x}{2} + \frac{11}{42}$

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