Finite Math Examples

$8 x + 5 y = 6 f (x)$

Step 1

Subtract $6 f x$ from both sides of the equation.

$8 x + 5 y - 6 f x = 0$

Step 2

Subtract $5 y$ from both sides of the equation.

$8 x - 6 f x = - 5 y$

Step 3

Factor $2 x$ out of $8 x - 6 f x$ .

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Step 3.1

Factor $2 x$ out of $8 x$ .

$2 x (4) - 6 f x = - 5 y$

Step 3.2

Factor $2 x$ out of $- 6 f x$ .

$2 x (4) + 2 x (- 3 f) = - 5 y$

Step 3.3

Factor $2 x$ out of $2 x (4) + 2 x (- 3 f)$ .

$2 x (4 - 3 f) = - 5 y$

Step 4

Divide each term in $2 x (4 - 3 f) = - 5 y$ by $2 (4 - 3 f)$ and simplify.

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Step 4.1

Divide each term in $2 x (4 - 3 f) = - 5 y$ by $2 (4 - 3 f)$ .

$\frac{2 x (4 - 3 f)}{2 (4 - 3 f)} = \frac{- 5 y}{2 (4 - 3 f)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 x (4 - 3 f)}{2 (4 - 3 f)} = \frac{- 5 y}{2 (4 - 3 f)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{x (4 - 3 f)}{4 - 3 f} = \frac{- 5 y}{2 (4 - 3 f)}$

Step 4.2.2

Cancel the common factor of $4 - 3 f$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{x (4 - 3 f)}{4 - 3 f} = \frac{- 5 y}{2 (4 - 3 f)}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 5 y}{2 (4 - 3 f)}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$x = - \frac{5 y}{2 (4 - 3 f)}$