Finite Math Examples

$(2 x - 1) (x + 4) = k (x - 1) + 3$

Step 1

Rewrite the equation as $k (x - 1) + 3 = (2 x - 1) (x + 4)$ .

$k (x - 1) + 3 = (2 x - 1) (x + 4)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$k x + k \cdot - 1 + 3 = (2 x - 1) (x + 4)$

Step 2.2

Move $- 1$ to the left of $k$ .

$k x - 1 \cdot k + 3 = (2 x - 1) (x + 4)$

Step 2.3

Rewrite $- 1 k$ as $- k$ .

$k x - k + 3 = (2 x - 1) (x + 4)$

Step 3

Simplify $(2 x - 1) (x + 4)$ .

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Step 3.1

Expand $(2 x - 1) (x + 4)$ using the FOIL Method.

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Step 3.1.1

Apply the distributive property.

$k x - k + 3 = 2 x (x + 4) - 1 (x + 4)$

Step 3.1.2

Apply the distributive property.

$k x - k + 3 = 2 x \cdot x + 2 x \cdot 4 - 1 (x + 4)$

Step 3.1.3

Apply the distributive property.

$k x - k + 3 = 2 x \cdot x + 2 x \cdot 4 - 1 x - 1 \cdot 4$

Step 3.2

Simplify and combine like terms.

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 3.2.1.1.1

Move $x$ .

$k x - k + 3 = 2 (x \cdot x) + 2 x \cdot 4 - 1 x - 1 \cdot 4$

Step 3.2.1.1.2

Multiply $x$ by $x$ .

$k x - k + 3 = 2 x^{2} + 2 x \cdot 4 - 1 x - 1 \cdot 4$

Step 3.2.1.2

Multiply $4$ by $2$ .

$k x - k + 3 = 2 x^{2} + 8 x - 1 x - 1 \cdot 4$

Step 3.2.1.3

Rewrite $- 1 x$ as $- x$ .

$k x - k + 3 = 2 x^{2} + 8 x - x - 1 \cdot 4$

Step 3.2.1.4

Multiply $- 1$ by $4$ .

$k x - k + 3 = 2 x^{2} + 8 x - x - 4$

Step 3.2.2

Subtract $x$ from $8 x$ .

$k x - k + 3 = 2 x^{2} + 7 x - 4$

Step 4

Move all terms not containing $k$ to the right side of the equation.

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Step 4.1

Subtract $3$ from both sides of the equation.

$k x - k = 2 x^{2} + 7 x - 4 - 3$

Step 4.2

Subtract $3$ from $- 4$ .

$k x - k = 2 x^{2} + 7 x - 7$

Step 5

Factor $k$ out of $k x - k$ .

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Step 5.1

Factor $k$ out of $k x$ .

$k (x) - k = 2 x^{2} + 7 x - 7$

Step 5.2

Factor $k$ out of $- k$ .

$k (x) + k \cdot - 1 = 2 x^{2} + 7 x - 7$

Step 5.3

Factor $k$ out of $k (x) + k \cdot - 1$ .

$k (x - 1) = 2 x^{2} + 7 x - 7$

Step 6

Divide each term in $k (x - 1) = 2 x^{2} + 7 x - 7$ by $x - 1$ and simplify.

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Step 6.1

Divide each term in $k (x - 1) = 2 x^{2} + 7 x - 7$ by $x - 1$ .

$\frac{k (x - 1)}{x - 1} = \frac{2 x^{2}}{x - 1} + \frac{7 x}{x - 1} + \frac{- 7}{x - 1}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $x - 1$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{k (x - 1)}{x - 1} = \frac{2 x^{2}}{x - 1} + \frac{7 x}{x - 1} + \frac{- 7}{x - 1}$

Step 6.2.1.2

Divide $k$ by $1$ .

$k = \frac{2 x^{2}}{x - 1} + \frac{7 x}{x - 1} + \frac{- 7}{x - 1}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Combine the numerators over the common denominator.

$k = \frac{2 x^{2} + 7 x - 7}{x - 1}$