Algebra Examples

$\frac{1}{2} \cdot (n - 4) - 3 = 3 - (2 n + 3)$

Step 1

Simplify $\frac{1}{2} \cdot (n - 4) - 3$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{2} n + \frac{1}{2} \cdot - 4 - 3 = 3 - (2 n + 3)$

Step 1.1.2

Combine $\frac{1}{2}$ and $n$ .

$\frac{n}{2} + \frac{1}{2} \cdot - 4 - 3 = 3 - (2 n + 3)$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Factor $2$ out of $- 4$ .

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

Step 1.1.3.2

Cancel the common factor.

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

Step 1.1.3.3

Rewrite the expression.

$\frac{n}{2} - 2 - 3 = 3 - (2 n + 3)$

Step 1.2

Subtract $3$ from $- 2$ .

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

Step 2

Simplify $3 - (2 n + 3)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$\frac{n}{2} - 5 = 3 - (2 n) - 1 \cdot 3$

Step 2.1.2

Multiply $2$ by $- 1$ .

$\frac{n}{2} - 5 = 3 - 2 n - 1 \cdot 3$

Step 2.1.3

Multiply $- 1$ by $3$ .

$\frac{n}{2} - 5 = 3 - 2 n - 3$

Step 2.2

Combine the opposite terms in $3 - 2 n - 3$ .

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Step 2.2.1

Subtract $3$ from $3$ .

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

Step 2.2.2

Add $- 2 n$ and $0$ .

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

Step 3

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

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Step 3.1

Add $2 n$ to both sides of the equation.

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

Step 3.2

To write $2 n$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3.3

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

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $n$ out of $n + 2 n \cdot 2$ .

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Step 3.5.1.1.1

Raise $n$ to the power of $1$ .

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

Step 3.5.1.1.2

Factor $n$ out of $n^{1}$ .

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

Step 3.5.1.1.3

Factor $n$ out of $2 n \cdot 2$ .

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

Step 3.5.1.1.4

Factor $n$ out of $n \cdot 1 + n (2 \cdot 2)$ .

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

Step 3.5.1.2

Multiply $2$ by $2$ .

$\frac{n (1 + 4)}{2} - 5 = 0$

Step 3.5.1.3

Add $1$ and $4$ .

$\frac{n \cdot 5}{2} - 5 = 0$

Step 3.5.2

Move $5$ to the left of $n$ .

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

Step 4

Add $5$ to both sides of the equation.

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

Step 5

Multiply both sides of the equation by $\frac{2}{5}$ .

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

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

Simplify $\frac{2}{5} \cdot \frac{5 n}{2}$ .

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Step 6.1.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1.1

Cancel the common factor.

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

Step 6.1.1.1.2

Rewrite the expression.

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

Step 6.1.1.2

Cancel the common factor of $5$ .

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Step 6.1.1.2.1

Factor $5$ out of $5 n$ .

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

Step 6.1.1.2.2

Cancel the common factor.

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

Step 6.1.1.2.3

Rewrite the expression.

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

Step 6.2

Simplify the right side.

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Step 6.2.1

Cancel the common factor of $5$ .

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Step 6.2.1.1

Cancel the common factor.

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

Step 6.2.1.2

Rewrite the expression.

$n = 2$