Algebra Examples

$\frac{2}{5} (8 n - 5) = - \frac{9}{5} n$

Step 1

Simplify $\frac{2}{5} \cdot (8 n - 5)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{2}{5} \cdot (8 n - 5) = - \frac{9}{5} n$

Step 1.2

Simplify by adding zeros.

$\frac{2}{5} \cdot (8 n - 5) = - \frac{9}{5} n$

Step 1.3

Apply the distributive property.

$\frac{2}{5} (8 n) + \frac{2}{5} \cdot - 5 = - \frac{9}{5} n$

Step 1.4

Multiply $\frac{2}{5} (8 n)$ .

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Step 1.4.1

Combine $8$ and $\frac{2}{5}$ .

$\frac{8 \cdot 2}{5} n + \frac{2}{5} \cdot - 5 = - \frac{9}{5} n$

Step 1.4.2

Multiply $8$ by $2$ .

$\frac{16}{5} n + \frac{2}{5} \cdot - 5 = - \frac{9}{5} n$

Step 1.4.3

Combine $\frac{16}{5}$ and $n$ .

$\frac{16 n}{5} + \frac{2}{5} \cdot - 5 = - \frac{9}{5} n$

Step 1.5

Cancel the common factor of $5$ .

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Step 1.5.1

Factor $5$ out of $- 5$ .

$\frac{16 n}{5} + \frac{2}{5} \cdot (5 (- 1)) = - \frac{9}{5} n$

Step 1.5.2

Cancel the common factor.

$\frac{16 n}{5} + \frac{2}{5} \cdot (5 \cdot - 1) = - \frac{9}{5} n$

Step 1.5.3

Rewrite the expression.

$\frac{16 n}{5} + 2 \cdot - 1 = - \frac{9}{5} n$

Step 1.6

Multiply $2$ by $- 1$ .

$\frac{16 n}{5} - 2 = - \frac{9}{5} n$

Step 2

Simplify $- \frac{9}{5} n$ .

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Step 2.1

Combine $n$ and $\frac{9}{5}$ .

$\frac{16 n}{5} - 2 = - \frac{n \cdot 9}{5}$

Step 2.2

Move $9$ to the left of $n$ .

$\frac{16 n}{5} - 2 = - \frac{9 n}{5}$

Step 3

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

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Step 3.1

Add $\frac{9 n}{5}$ to both sides of the equation.

$\frac{16 n}{5} - 2 + \frac{9 n}{5} = 0$

Step 3.2

Combine the numerators over the common denominator.

$- 2 + \frac{16 n + 9 n}{5} = 0$

Step 3.3

Add $16 n$ and $9 n$ .

$- 2 + \frac{25 n}{5} = 0$

Step 3.4

Cancel the common factor of $25$ and $5$ .

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Step 3.4.1

Factor $5$ out of $25 n$ .

$- 2 + \frac{5 (5 n)}{5} = 0$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $5$ out of $5$ .

$- 2 + \frac{5 (5 n)}{5 (1)} = 0$

Step 3.4.2.2

Cancel the common factor.

$- 2 + \frac{5 (5 n)}{5 \cdot 1} = 0$

Step 3.4.2.3

Rewrite the expression.

$- 2 + \frac{5 n}{1} = 0$

Step 3.4.2.4

Divide $5 n$ by $1$ .

$- 2 + 5 n = 0$

Step 4

Add $2$ to both sides of the equation.

$5 n = 2$

Step 5

Divide each term in $5 n = 2$ by $5$ and simplify.

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Step 5.1

Divide each term in $5 n = 2$ by $5$ .

$\frac{5 n}{5} = \frac{2}{5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{5 n}{5} = \frac{2}{5}$

Step 5.2.1.2

Divide $n$ by $1$ .

$n = \frac{2}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$n = \frac{2}{5}$

Decimal Form:

$n = 0.4$