Algebra Examples

$2 - \frac{8}{x} = 6$

Step 1

Subtract $6$ from both sides of the equation.

$2 - \frac{8}{x} - 6 = 0$

Step 2

Subtract $6$ from $2$ .

$- \frac{8}{x} - 4 = 0$

Step 3

Factor $- 4$ out of $- \frac{8}{x} - 4$ .

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Step 3.1

Factor $- 4$ out of $- \frac{8}{x}$ .

$- 4 (- \frac{- 2}{x}) - 4 = 0$

Step 3.2

Factor $- 4$ out of $- 4$ .

$- 4 (- \frac{- 2}{x}) - 4 \cdot 1 = 0$

Step 3.3

Factor $- 4$ out of $- 4 (- \frac{- 2}{x}) - 4 (1)$ .

$- 4 (- \frac{- 2}{x} + 1) = 0$

Step 4

Move the negative in front of the fraction.

$- 4 (\frac{2}{x} + 1) = 0$

Step 5

Write $1$ as a fraction with a common denominator.

$- 4 (\frac{2}{x} + \frac{x}{x}) = 0$

Step 6

Combine the numerators over the common denominator.

$- 4 \frac{2 + x}{x} = 0$

Step 7

Simplify $- 4 \frac{2 + x}{x}$ .

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Step 7.1

Combine $- 4$ and $\frac{2 + x}{x}$ .

$\frac{- 4 (2 + x)}{x} = 0$

Step 7.2

Move the negative in front of the fraction.

$- \frac{4 (2 + x)}{x} = 0$

Step 8

Set the numerator equal to zero.

$4 (2 + x) = 0$

Step 9

Solve the equation for $x$ .

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Step 9.1

Divide each term in $4 (2 + x) = 0$ by $4$ and simplify.

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Step 9.1.1

Divide each term in $4 (2 + x) = 0$ by $4$ .

$\frac{4 (2 + x)}{4} = \frac{0}{4}$

Step 9.1.2

Simplify the left side.

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Step 9.1.2.1

Cancel the common factor of $4$ .

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Step 9.1.2.1.1

Cancel the common factor.

$\frac{4 (2 + x)}{4} = \frac{0}{4}$

Step 9.1.2.1.2

Divide $2 + x$ by $1$ .

$2 + x = \frac{0}{4}$

Step 9.1.3

Simplify the right side.

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Step 9.1.3.1

Divide $0$ by $4$ .

$2 + x = 0$

Step 9.2

Subtract $2$ from both sides of the equation.

$x = - 2$