Algebra Examples

$8 - (n + \frac{1}{7} x) = 3 n$ for $n$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{7}$ and $x$ .

$8 - (n + \frac{x}{7}) = 3 n$

Step 1.2

Apply the distributive property.

$8 - n - \frac{x}{7} = 3 n$

Step 2

Move all terms containing $n$ to the left side of the equation.

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Step 2.1

Subtract $3 n$ from both sides of the equation.

$8 - n - \frac{x}{7} - 3 n = 0$

Step 2.2

Subtract $3 n$ from $- n$ .

$8 - 4 n - \frac{x}{7} = 0$

Step 3

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

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Step 3.1

Subtract $8$ from both sides of the equation.

$- 4 n - \frac{x}{7} = - 8$

Step 3.2

Add $\frac{x}{7}$ to both sides of the equation.

$- 4 n = - 8 + \frac{x}{7}$

Step 4

Divide each term in $- 4 n = - 8 + \frac{x}{7}$ by $- 4$ and simplify.

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Step 4.1

Divide each term in $- 4 n = - 8 + \frac{x}{7}$ by $- 4$ .

$\frac{- 4 n}{- 4} = \frac{- 8}{- 4} + \frac{\frac{x}{7}}{- 4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 4 n}{- 4} = \frac{- 8}{- 4} + \frac{\frac{x}{7}}{- 4}$

Step 4.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 8}{- 4} + \frac{\frac{x}{7}}{- 4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Divide $- 8$ by $- 4$ .

$n = 2 + \frac{\frac{x}{7}}{- 4}$

Step 4.3.1.2

Multiply the numerator by the reciprocal of the denominator.

$n = 2 + \frac{x}{7} \cdot \frac{1}{- 4}$

Step 4.3.1.3

Move the negative in front of the fraction.

$n = 2 + \frac{x}{7} (- \frac{1}{4})$

Step 4.3.1.4

Multiply $\frac{x}{7} (- \frac{1}{4})$ .

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Step 4.3.1.4.1

Multiply $\frac{x}{7}$ by $\frac{1}{4}$ .

$n = 2 - \frac{x}{7 \cdot 4}$

Step 4.3.1.4.2

Multiply $7$ by $4$ .

$n = 2 - \frac{x}{28}$