Algebra Examples

$\frac{6 (c x + 6)}{3} = 8 x - 10$

Step 1

Cancel the common factor of $6$ and $3$ .

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Step 1.1

Factor $3$ out of $6 (c x + 6)$ .

$\frac{3 (2 (c x + 6))}{3} = 8 x - 10$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $3$ .

$\frac{3 (2 (c x + 6))}{3 (1)} = 8 x - 10$

Step 1.2.2

Cancel the common factor.

$\frac{3 (2 (c x + 6))}{3 \cdot 1} = 8 x - 10$

Step 1.2.3

Rewrite the expression.

$\frac{2 (c x + 6)}{1} = 8 x - 10$

Step 1.2.4

Divide $2 (c x + 6)$ by $1$ .

$2 (c x + 6) = 8 x - 10$

Step 2

Solve for $c$ .

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Step 2.1

Divide each term in $2 (c x + 6) = 8 x - 10$ by $2$ and simplify.

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Step 2.1.1

Divide each term in $2 (c x + 6) = 8 x - 10$ by $2$ .

$\frac{2 (c x + 6)}{2} = \frac{8 x}{2} + \frac{- 10}{2}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $2$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{2 (c x + 6)}{2} = \frac{8 x}{2} + \frac{- 10}{2}$

Step 2.1.2.1.2

Divide $c x + 6$ by $1$ .

$c x + 6 = \frac{8 x}{2} + \frac{- 10}{2}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

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

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Step 2.1.3.1.1.1

Factor $2$ out of $8 x$ .

$c x + 6 = \frac{2 (4 x)}{2} + \frac{- 10}{2}$

Step 2.1.3.1.1.2

Cancel the common factors.

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Step 2.1.3.1.1.2.1

Factor $2$ out of $2$ .

$c x + 6 = \frac{2 (4 x)}{2 (1)} + \frac{- 10}{2}$

Step 2.1.3.1.1.2.2

Cancel the common factor.

$c x + 6 = \frac{2 (4 x)}{2 \cdot 1} + \frac{- 10}{2}$

Step 2.1.3.1.1.2.3

Rewrite the expression.

$c x + 6 = \frac{4 x}{1} + \frac{- 10}{2}$

Step 2.1.3.1.1.2.4

Divide $4 x$ by $1$ .

$c x + 6 = 4 x + \frac{- 10}{2}$

Step 2.1.3.1.2

Divide $- 10$ by $2$ .

$c x + 6 = 4 x - 5$

Step 2.2

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

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Step 2.2.1

Subtract $6$ from both sides of the equation.

$c x = 4 x - 5 - 6$

Step 2.2.2

Subtract $6$ from $- 5$ .

$c x = 4 x - 11$

Step 2.3

Divide each term in $c x = 4 x - 11$ by $x$ and simplify.

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Step 2.3.1

Divide each term in $c x = 4 x - 11$ by $x$ .

$\frac{c x}{x} = \frac{4 x}{x} + \frac{- 11}{x}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $x$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{c x}{x} = \frac{4 x}{x} + \frac{- 11}{x}$

Step 2.3.2.1.2

Divide $c$ by $1$ .

$c = \frac{4 x}{x} + \frac{- 11}{x}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Cancel the common factor of $x$ .

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Step 2.3.3.1.1.1

Cancel the common factor.

$c = \frac{4 x}{x} + \frac{- 11}{x}$

Step 2.3.3.1.1.2

Divide $4$ by $1$ .

$c = 4 + \frac{- 11}{x}$

Step 2.3.3.1.2

Move the negative in front of the fraction.

$c = 4 - \frac{11}{x}$