Algebra Examples

$- \frac{2}{5} (n + 2) = 6$

Step 1

Multiply both sides of the equation by $- \frac{5}{2}$ .

$- \frac{5}{2} (- \frac{2}{5} \cdot (n + 2)) = - \frac{5}{2} \cdot 6$

Step 2

Simplify both sides of the equation.

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Simplify the left side.

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Simplify $- \frac{5}{2} (- \frac{2}{5} \cdot (n + 2))$ .

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Apply the distributive property.

$- \frac{5}{2} (- \frac{2}{5} n - \frac{2}{5} \cdot 2) = - \frac{5}{2} \cdot 6$

Combine $n$ and $\frac{2}{5}$ .

$- \frac{5}{2} (- \frac{n \cdot 2}{5} - \frac{2}{5} \cdot 2) = - \frac{5}{2} \cdot 6$

Multiply $- \frac{2}{5} \cdot 2$ .

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Multiply $2$ by $- 1$ .

$- \frac{5}{2} (- \frac{n \cdot 2}{5} - 2 (\frac{2}{5})) = - \frac{5}{2} \cdot 6$

Combine $- 2$ and $\frac{2}{5}$ .

$- \frac{5}{2} (- \frac{n \cdot 2}{5} + \frac{- 2 \cdot 2}{5}) = - \frac{5}{2} \cdot 6$

Multiply $- 2$ by $2$ .

$- \frac{5}{2} (- \frac{n \cdot 2}{5} + \frac{- 4}{5}) = - \frac{5}{2} \cdot 6$

Simplify each term.

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Move $2$ to the left of $n$ .

$- \frac{5}{2} (- \frac{2 \cdot n}{5} + \frac{- 4}{5}) = - \frac{5}{2} \cdot 6$

Move the negative in front of the fraction.

$- \frac{5}{2} (- \frac{2 n}{5} - \frac{4}{5}) = - \frac{5}{2} \cdot 6$

Simplify terms.

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Apply the distributive property.

$- \frac{5}{2} (- \frac{2 n}{5}) - \frac{5}{2} (- \frac{4}{5}) = - \frac{5}{2} \cdot 6$

Cancel the common factor of $5$ .

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Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{- 5}{2} (- \frac{2 n}{5}) - \frac{5}{2} (- \frac{4}{5}) = - \frac{5}{2} \cdot 6$

Move the leading negative in $- \frac{2 n}{5}$ into the numerator.

$\frac{- 5}{2} \cdot \frac{- 2 n}{5} - \frac{5}{2} (- \frac{4}{5}) = - \frac{5}{2} \cdot 6$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{2} \cdot \frac{- 2 n}{5} - \frac{5}{2} (- \frac{4}{5}) = - \frac{5}{2} \cdot 6$

Cancel the common factor.

$\frac{5 \cdot - 1}{2} \cdot \frac{- 2 n}{5} - \frac{5}{2} (- \frac{4}{5}) = - \frac{5}{2} \cdot 6$

Rewrite the expression.

$\frac{- 1}{2} (- 2 n) - \frac{5}{2} (- \frac{4}{5}) = - \frac{5}{2} \cdot 6$

Cancel the common factor of $2$ .

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Factor $2$ out of $- 2 n$ .

$\frac{- 1}{2} (2 (- n)) - \frac{5}{2} (- \frac{4}{5}) = - \frac{5}{2} \cdot 6$

Cancel the common factor.

$\frac{- 1}{2} (2 (- n)) - \frac{5}{2} (- \frac{4}{5}) = - \frac{5}{2} \cdot 6$

Rewrite the expression.

$- - n - \frac{5}{2} (- \frac{4}{5}) = - \frac{5}{2} \cdot 6$

Multiply.

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Multiply $- 1$ by $- 1$ .

$1 n - \frac{5}{2} (- \frac{4}{5}) = - \frac{5}{2} \cdot 6$

Multiply $n$ by $1$ .

$n - \frac{5}{2} (- \frac{4}{5}) = - \frac{5}{2} \cdot 6$

Cancel the common factor of $5$ .

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Move the leading negative in $- \frac{5}{2}$ into the numerator.

$n + \frac{- 5}{2} (- \frac{4}{5}) = - \frac{5}{2} \cdot 6$

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$n + \frac{- 5}{2} \cdot \frac{- 4}{5} = - \frac{5}{2} \cdot 6$

Factor $5$ out of $- 5$ .

$n + \frac{5 (- 1)}{2} \cdot \frac{- 4}{5} = - \frac{5}{2} \cdot 6$

Cancel the common factor.

$n + \frac{5 \cdot - 1}{2} \cdot \frac{- 4}{5} = - \frac{5}{2} \cdot 6$

Rewrite the expression.

$n + \frac{- 1}{2} \cdot - 4 = - \frac{5}{2} \cdot 6$

Cancel the common factor of $2$ .

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Factor $2$ out of $- 4$ .

$n + \frac{- 1}{2} \cdot (2 (- 2)) = - \frac{5}{2} \cdot 6$

Cancel the common factor.

$n + \frac{- 1}{2} \cdot (2 \cdot - 2) = - \frac{5}{2} \cdot 6$

Rewrite the expression.

$n - - 2 = - \frac{5}{2} \cdot 6$

Multiply $- 1$ by $- 2$ .

$n + 2 = - \frac{5}{2} \cdot 6$

Simplify the right side.

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Simplify $- \frac{5}{2} \cdot 6$ .

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Cancel the common factor of $2$ .

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Move the leading negative in $- \frac{5}{2}$ into the numerator.

$n + 2 = \frac{- 5}{2} \cdot 6$

Factor $2$ out of $6$ .

$n + 2 = \frac{- 5}{2} \cdot (2 (3))$

Cancel the common factor.

$n + 2 = \frac{- 5}{2} \cdot (2 \cdot 3)$

Rewrite the expression.

$n + 2 = - 5 \cdot 3$

Multiply $- 5$ by $3$ .

$n + 2 = - 15$

Step 3

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

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Subtract $2$ from both sides of the equation.

$n = - 15 - 2$

Subtract $2$ from $- 15$ .

$n = - 17$