Algebra Examples

$\frac{3}{5} n + \frac{9}{10} = - \frac{1}{5} n - \frac{23}{10}$

Step 1

Combine $\frac{3}{5}$ and $n$ .

$\frac{3 n}{5} + \frac{9}{10} = - \frac{1}{5} n - \frac{23}{10}$

Step 2

Combine $n$ and $\frac{1}{5}$ .

$\frac{3 n}{5} + \frac{9}{10} = - \frac{n}{5} - \frac{23}{10}$

Step 3

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

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Step 3.1

Add $\frac{n}{5}$ to both sides of the equation.

$\frac{3 n}{5} + \frac{9}{10} + \frac{n}{5} = - \frac{23}{10}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3 n + n}{5} + \frac{9}{10} = - \frac{23}{10}$

Step 3.3

Add $3 n$ and $n$ .

$\frac{4 n}{5} + \frac{9}{10} = - \frac{23}{10}$

Step 4

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

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Step 4.1

Subtract $\frac{9}{10}$ from both sides of the equation.

$\frac{4 n}{5} = - \frac{23}{10} - \frac{9}{10}$

Step 4.2

Combine the numerators over the common denominator.

$\frac{4 n}{5} = \frac{- 23 - 9}{10}$

Step 4.3

Subtract $9$ from $- 23$ .

$\frac{4 n}{5} = \frac{- 32}{10}$

Step 4.4

Cancel the common factor of $- 32$ and $10$ .

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Step 4.4.1

Factor $2$ out of $- 32$ .

$\frac{4 n}{5} = \frac{2 (- 16)}{10}$

Step 4.4.2

Cancel the common factors.

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Step 4.4.2.1

Factor $2$ out of $10$ .

$\frac{4 n}{5} = \frac{2 \cdot - 16}{2 \cdot 5}$

Step 4.4.2.2

Cancel the common factor.

$\frac{4 n}{5} = \frac{2 \cdot - 16}{2 \cdot 5}$

Step 4.4.2.3

Rewrite the expression.

$\frac{4 n}{5} = \frac{- 16}{5}$

Step 4.5

Move the negative in front of the fraction.

$\frac{4 n}{5} = - \frac{16}{5}$

Step 5

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$4 n = - 16$

Step 6

Divide each term in $4 n = - 16$ by $4$ and simplify.

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Step 6.1

Divide each term in $4 n = - 16$ by $4$ .

$\frac{4 n}{4} = \frac{- 16}{4}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $4$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{4 n}{4} = \frac{- 16}{4}$

Step 6.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 16}{4}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 16$ by $4$ .

$n = - 4$