Basic Math Examples

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

Step 1

Simplify $\frac{1}{2} \cdot (2 n - 5)$ .

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $2 n$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

$n + \frac{1}{2} \cdot - 5 = 4 n - 1$

Step 1.5

Combine $\frac{1}{2}$ and $- 5$ .

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

Step 1.6

Move the negative in front of the fraction.

$n - \frac{5}{2} = 4 n - 1$

Step 2

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

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Step 2.1

Subtract $4 n$ from both sides of the equation.

$n - \frac{5}{2} - 4 n = - 1$

Step 2.2

Subtract $4 n$ from $n$ .

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

Step 3

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

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Step 3.1

Add $\frac{5}{2}$ to both sides of the equation.

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

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3.3

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

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $2$ .

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

Step 3.5.2

Add $- 2$ and $5$ .

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

Step 4

Divide each term in $- 3 n = \frac{3}{2}$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 n = \frac{3}{2}$ by $- 3$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $n$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 4.3.2

Cancel the common factor of $3$ .

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Step 4.3.2.1

Factor $3$ out of $- 3$ .

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

Step 4.3.2.2

Cancel the common factor.

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

Step 4.3.2.3

Rewrite the expression.

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

Step 4.3.3

Multiply $\frac{1}{2}$ by $\frac{1}{- 1}$ .

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

Step 4.3.4

Simplify the expression.

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Step 4.3.4.1

Multiply $2$ by $- 1$ .

$n = \frac{1}{- 2}$

Step 4.3.4.2

Move the negative in front of the fraction.

$n = - \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{1}{2}$

Decimal Form:

$n = - 0.5$