Finite Math Examples

$6 x - 2 k x - 8 k = 15$

Step 1

Add $8 k$ to both sides of the equation.

$6 x - 2 k x = 15 + 8 k$

Step 2

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

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Step 2.1

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

$2 x (3) - 2 k x = 15 + 8 k$

Step 2.2

Factor $2 x$ out of $- 2 k x$ .

$2 x (3) + 2 x (- k) = 15 + 8 k$

Step 2.3

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

$2 x (3 - k) = 15 + 8 k$

Step 3

Divide each term in $2 x (3 - k) = 15 + 8 k$ by $2 (3 - k)$ and simplify.

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Step 3.1

Divide each term in $2 x (3 - k) = 15 + 8 k$ by $2 (3 - k)$ .

$\frac{2 x (3 - k)}{2 (3 - k)} = \frac{15}{2 (3 - k)} + \frac{8 k}{2 (3 - k)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 x (3 - k)}{2 (3 - k)} = \frac{15}{2 (3 - k)} + \frac{8 k}{2 (3 - k)}$

Step 3.2.1.2

Rewrite the expression.

$\frac{x (3 - k)}{3 - k} = \frac{15}{2 (3 - k)} + \frac{8 k}{2 (3 - k)}$

Step 3.2.2

Cancel the common factor of $3 - k$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{x (3 - k)}{3 - k} = \frac{15}{2 (3 - k)} + \frac{8 k}{2 (3 - k)}$

Step 3.2.2.2

Divide $x$ by $1$ .

$x = \frac{15}{2 (3 - k)} + \frac{8 k}{2 (3 - k)}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $8$ and $2$ .

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Step 3.3.1.1

Factor $2$ out of $8 k$ .

$x = \frac{15}{2 (3 - k)} + \frac{2 (4 k)}{2 (3 - k)}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Cancel the common factor.

$x = \frac{15}{2 (3 - k)} + \frac{2 (4 k)}{2 (3 - k)}$

Step 3.3.1.2.2

Rewrite the expression.

$x = \frac{15}{2 (3 - k)} + \frac{4 k}{3 - k}$

Step 3.3.2

To write $\frac{4 k}{3 - k}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{15}{2 (3 - k)} + \frac{4 k}{3 - k} \cdot \frac{2}{2}$

Step 3.3.3

Write each expression with a common denominator of $2 (3 - k)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.3.1

Multiply $\frac{4 k}{3 - k}$ by $\frac{2}{2}$ .

$x = \frac{15}{2 (3 - k)} + \frac{4 k \cdot 2}{(3 - k) \cdot 2}$

Step 3.3.3.2

Reorder the factors of $(3 - k) \cdot 2$ .

$x = \frac{15}{2 (3 - k)} + \frac{4 k \cdot 2}{2 (3 - k)}$

Step 3.3.4

Combine the numerators over the common denominator.

$x = \frac{15 + 4 k \cdot 2}{2 (3 - k)}$

Step 3.3.5

Multiply $2$ by $4$ .

$x = \frac{15 + 8 k}{2 (3 - k)}$