Algebra Examples

$\frac{3}{5} (n + 25) = 10 + \frac{2}{5} n$

Step 1

Simplify $\frac{3}{5} \cdot (n + 25)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{3}{5} \cdot (n + 25) = 10 + \frac{2}{5} n$

Step 1.2

Simplify by adding zeros.

$\frac{3}{5} \cdot (n + 25) = 10 + \frac{2}{5} n$

Step 1.3

Apply the distributive property.

$\frac{3}{5} n + \frac{3}{5} \cdot 25 = 10 + \frac{2}{5} n$

Step 1.4

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

$\frac{3 n}{5} + \frac{3}{5} \cdot 25 = 10 + \frac{2}{5} n$

Step 1.5

Cancel the common factor of $5$ .

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Step 1.5.1

Factor $5$ out of $25$ .

$\frac{3 n}{5} + \frac{3}{5} \cdot (5 (5)) = 10 + \frac{2}{5} n$

Step 1.5.2

Cancel the common factor.

$\frac{3 n}{5} + \frac{3}{5} \cdot (5 \cdot 5) = 10 + \frac{2}{5} n$

Step 1.5.3

Rewrite the expression.

$\frac{3 n}{5} + 3 \cdot 5 = 10 + \frac{2}{5} n$

Step 1.6

Multiply $3$ by $5$ .

$\frac{3 n}{5} + 15 = 10 + \frac{2}{5} n$

Step 2

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

$\frac{3 n}{5} + 15 = 10 + \frac{2 n}{5}$

Step 3

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

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Step 3.1

Subtract $\frac{2 n}{5}$ from both sides of the equation.

$\frac{3 n}{5} + 15 - \frac{2 n}{5} = 10$

Step 3.2

Combine the numerators over the common denominator.

$15 + \frac{3 n - 2 n}{5} = 10$

Step 3.3

Subtract $2 n$ from $3 n$ .

$15 + \frac{n}{5} = 10$

Step 4

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

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Step 4.1

Subtract $15$ from both sides of the equation.

$\frac{n}{5} = 10 - 15$

Step 4.2

Subtract $15$ from $10$ .

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

Step 5

Multiply both sides of the equation by $5$ .

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

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $5$ .

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Step 6.1.1.1

Cancel the common factor.

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

Step 6.1.1.2

Rewrite the expression.

$n = 5 \cdot - 5$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $5$ by $- 5$ .

$n = - 25$