Solve for n 2/5n+1/10=1/2(n+4)

$\frac{2}{5} n + \frac{1}{10} = \frac{1}{2} (n + 4)$

Step 1

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

$\frac{2 n}{5} + \frac{1}{10} = \frac{1}{2} \cdot (n + 4)$

Step 2

Simplify $\frac{1}{2} \cdot (n + 4)$ .

Apply the distributive property.

$\frac{2 n}{5} + \frac{1}{10} = \frac{1}{2} n + \frac{1}{2} \cdot 4$

Combine $\frac{1}{2}$ and $n$ .

$\frac{2 n}{5} + \frac{1}{10} = \frac{n}{2} + \frac{1}{2} \cdot 4$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{2 n}{5} + \frac{1}{10} = \frac{n}{2} + \frac{1}{2} \cdot (2 (2))$

Cancel the common factor.

$\frac{2 n}{5} + \frac{1}{10} = \frac{n}{2} + \frac{1}{2} \cdot (2 \cdot 2)$

Rewrite the expression.

$\frac{2 n}{5} + \frac{1}{10} = \frac{n}{2} + 2$

Step 3

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

Subtract $\frac{n}{2}$ from both sides of the equation.

$\frac{2 n}{5} + \frac{1}{10} - \frac{n}{2} = 2$

To write $\frac{2 n}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 n}{5} \cdot \frac{2}{2} - \frac{n}{2} + \frac{1}{10} = 2$

To write $- \frac{n}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 n}{5} \cdot \frac{2}{2} - \frac{n}{2} \cdot \frac{5}{5} + \frac{1}{10} = 2$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 n}{5}$ by $\frac{2}{2}$ .

$\frac{2 n \cdot 2}{5 \cdot 2} - \frac{n}{2} \cdot \frac{5}{5} + \frac{1}{10} = 2$

Multiply $5$ by $2$ .

$\frac{2 n \cdot 2}{10} - \frac{n}{2} \cdot \frac{5}{5} + \frac{1}{10} = 2$

Multiply $\frac{n}{2}$ by $\frac{5}{5}$ .

$\frac{2 n \cdot 2}{10} - \frac{n \cdot 5}{2 \cdot 5} + \frac{1}{10} = 2$

Multiply $2$ by $5$ .

$\frac{2 n \cdot 2}{10} - \frac{n \cdot 5}{10} + \frac{1}{10} = 2$

Combine the numerators over the common denominator.

$\frac{2 n \cdot 2 - n \cdot 5}{10} + \frac{1}{10} = 2$

Combine the numerators over the common denominator.

$\frac{2 n \cdot 2 - n \cdot 5 + 1}{10} = 2$

Simplify each term.

Multiply $2$ by $2$ .

$\frac{4 n - n \cdot 5 + 1}{10} = 2$

Multiply $5$ by $- 1$ .

$\frac{4 n - 5 n + 1}{10} = 2$

Subtract $5 n$ from $4 n$ .

$\frac{- n + 1}{10} = 2$

Factor $- 1$ out of $- n$ .

$\frac{- (n) + 1}{10} = 2$

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- (n) - 1 (- 1)}{10} = 2$

Factor $- 1$ out of $- (n) - 1 (- 1)$ .

$\frac{- (n - 1)}{10} = 2$

Rewrite $- (n - 1)$ as $- 1 (n - 1)$ .

$\frac{- 1 (n - 1)}{10} = 2$

Move the negative in front of the fraction.

$- \frac{n - 1}{10} = 2$

Step 4

Multiply both sides of the equation by $- 10$ .

$- 10 (- \frac{n - 1}{10}) = - 10 \cdot 2$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 10 (- \frac{n - 1}{10})$ .

Cancel the common factor of $10$ .

Move the leading negative in $- \frac{n - 1}{10}$ into the numerator.

$- 10 \frac{- (n - 1)}{10} = - 10 \cdot 2$

Factor $10$ out of $- 10$ .

$10 (- 1) \frac{- (n - 1)}{10} = - 10 \cdot 2$

Cancel the common factor.

$10 \cdot - 1 \frac{- (n - 1)}{10} = - 10 \cdot 2$

Rewrite the expression.

$- - (n - 1) = - 10 \cdot 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (n - 1) = - 10 \cdot 2$

Multiply $n - 1$ by $1$ .

$n - 1 = - 10 \cdot 2$

Simplify the right side.

Multiply $- 10$ by $2$ .

$n - 1 = - 20$

Step 6

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

Add $1$ to both sides of the equation.

$n = - 20 + 1$

Add $- 20$ and $1$ .

$n = - 19$

Solve for n 2/5n+1/10=1/2(n+4)

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