Algebra Examples

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

Step 1

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

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Step 1.1

Subtract $3$ from both sides of the equation.

$\frac{3 n}{2} = 15 - 3$

Step 1.2

Subtract $3$ from $15$ .

$\frac{3 n}{2} = 12$

Step 2

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 n}{2} = \frac{2}{3} \cdot 12$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{2}{3} \cdot \frac{3 n}{2}$ .

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Step 3.1.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 n}{2} = \frac{2}{3} \cdot 12$

Step 3.1.1.1.2

Rewrite the expression.

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

Step 3.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.2.1

Factor $3$ out of $3 n$ .

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

Step 3.1.1.2.2

Cancel the common factor.

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

Step 3.1.1.2.3

Rewrite the expression.

$n = \frac{2}{3} \cdot 12$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{2}{3} \cdot 12$ .

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Step 3.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Factor $3$ out of $12$ .

$n = \frac{2}{3} \cdot (3 (4))$

Step 3.2.1.1.2

Cancel the common factor.

$n = \frac{2}{3} \cdot (3 \cdot 4)$

Step 3.2.1.1.3

Rewrite the expression.

$n = 2 \cdot 4$

Step 3.2.1.2

Multiply $2$ by $4$ .

$n = 8$