Algebra Examples

$\frac{1}{2} (10 + 12 n) = \frac{1}{3} (15 n + 15)$

Step 1

Simplify $\frac{1}{2} \cdot (10 + 12 n)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (10 + 12 n) = \frac{1}{3} \cdot (15 n + 15)$

Step 1.2

Simplify by adding zeros.

$\frac{1}{2} \cdot (10 + 12 n) = \frac{1}{3} \cdot (15 n + 15)$

Step 1.3

Apply the distributive property.

$\frac{1}{2} \cdot 10 + \frac{1}{2} (12 n) = \frac{1}{3} \cdot (15 n + 15)$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $10$ .

$\frac{1}{2} \cdot (2 (5)) + \frac{1}{2} (12 n) = \frac{1}{3} \cdot (15 n + 15)$

Step 1.4.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 5) + \frac{1}{2} (12 n) = \frac{1}{3} \cdot (15 n + 15)$

Step 1.4.3

Rewrite the expression.

$5 + \frac{1}{2} (12 n) = \frac{1}{3} \cdot (15 n + 15)$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $12 n$ .

$5 + \frac{1}{2} (2 (6 n)) = \frac{1}{3} \cdot (15 n + 15)$

Step 1.5.2

Cancel the common factor.

$5 + \frac{1}{2} (2 (6 n)) = \frac{1}{3} \cdot (15 n + 15)$

Step 1.5.3

Rewrite the expression.

$5 + 6 n = \frac{1}{3} \cdot (15 n + 15)$

Step 2

Simplify $\frac{1}{3} \cdot (15 n + 15)$ .

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Step 2.1

Apply the distributive property.

$5 + 6 n = \frac{1}{3} (15 n) + \frac{1}{3} \cdot 15$

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Factor $3$ out of $15 n$ .

$5 + 6 n = \frac{1}{3} (3 (5 n)) + \frac{1}{3} \cdot 15$

Step 2.2.2

Cancel the common factor.

$5 + 6 n = \frac{1}{3} (3 (5 n)) + \frac{1}{3} \cdot 15$

Step 2.2.3

Rewrite the expression.

$5 + 6 n = 5 n + \frac{1}{3} \cdot 15$

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Factor $3$ out of $15$ .

$5 + 6 n = 5 n + \frac{1}{3} \cdot (3 (5))$

Step 2.3.2

Cancel the common factor.

$5 + 6 n = 5 n + \frac{1}{3} \cdot (3 \cdot 5)$

Step 2.3.3

Rewrite the expression.

$5 + 6 n = 5 n + 5$

Step 3

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

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Step 3.1

Subtract $5 n$ from both sides of the equation.

$5 + 6 n - 5 n = 5$

Step 3.2

Subtract $5 n$ from $6 n$ .

$5 + n = 5$

Step 4

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

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Step 4.1

Subtract $5$ from both sides of the equation.

$n = 5 - 5$

Step 4.2

Subtract $5$ from $5$ .

$n = 0$