Trigonometry Examples

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

Step 1

Simplify $- \frac{3}{2} n + \frac{4}{3} n$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $n$ and $\frac{3}{2}$ .

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

Step 1.1.2

Move $3$ to the left of $n$ .

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

Step 1.1.3

Combine $\frac{4}{3}$ and $n$ .

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

Step 1.2

To write $- \frac{3 n}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.3

To write $\frac{4 n}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{3 n}{2}$ by $\frac{3}{3}$ .

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

Step 1.4.2

Multiply $2$ by $3$ .

$- \frac{3 n \cdot 3}{6} + \frac{4 n}{3} \cdot \frac{2}{2} = - \frac{1}{4}$

Step 1.4.3

Multiply $\frac{4 n}{3}$ by $\frac{2}{2}$ .

$- \frac{3 n \cdot 3}{6} + \frac{4 n \cdot 2}{3 \cdot 2} = - \frac{1}{4}$

Step 1.4.4

Multiply $3$ by $2$ .

$- \frac{3 n \cdot 3}{6} + \frac{4 n \cdot 2}{6} = - \frac{1}{4}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{- 3 n \cdot 3 + 4 n \cdot 2}{6} = - \frac{1}{4}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Factor $n$ out of $- 3 n \cdot 3 + 4 n \cdot 2$ .

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Step 1.6.1.1

Factor $n$ out of $- 3 n \cdot 3$ .

$\frac{n (- 3 \cdot 3) + 4 n \cdot 2}{6} = - \frac{1}{4}$

Step 1.6.1.2

Factor $n$ out of $4 n \cdot 2$ .

$\frac{n (- 3 \cdot 3) + n (4 \cdot 2)}{6} = - \frac{1}{4}$

Step 1.6.1.3

Factor $n$ out of $n (- 3 \cdot 3) + n (4 \cdot 2)$ .

$\frac{n (- 3 \cdot 3 + 4 \cdot 2)}{6} = - \frac{1}{4}$

Step 1.6.2

Multiply $- 3$ by $3$ .

$\frac{n (- 9 + 4 \cdot 2)}{6} = - \frac{1}{4}$

Step 1.6.3

Multiply $4$ by $2$ .

$\frac{n (- 9 + 8)}{6} = - \frac{1}{4}$

Step 1.6.4

Add $- 9$ and $8$ .

$\frac{n \cdot - 1}{6} = - \frac{1}{4}$

Step 1.7

Simplify the expression.

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Step 1.7.1

Move $- 1$ to the left of $n$ .

$\frac{- 1 \cdot n}{6} = - \frac{1}{4}$

Step 1.7.2

Move the negative in front of the fraction.

$- \frac{n}{6} = - \frac{1}{4}$

Step 2

Multiply both sides of the equation by $- 6$ .

$- 6 (- \frac{n}{6}) = - 6 (- \frac{1}{4})$

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 $- 6 (- \frac{n}{6})$ .

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Step 3.1.1.1

Cancel the common factor of $6$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{n}{6}$ into the numerator.

$- 6 \frac{- n}{6} = - 6 (- \frac{1}{4})$

Step 3.1.1.1.2

Factor $6$ out of $- 6$ .

$6 (- 1) \frac{- n}{6} = - 6 (- \frac{1}{4})$

Step 3.1.1.1.3

Cancel the common factor.

$6 \cdot - 1 \frac{- n}{6} = - 6 (- \frac{1}{4})$

Step 3.1.1.1.4

Rewrite the expression.

$- - n = - 6 (- \frac{1}{4})$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 n = - 6 (- \frac{1}{4})$

Step 3.1.1.2.2

Multiply $n$ by $1$ .

$n = - 6 (- \frac{1}{4})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- 6 (- \frac{1}{4})$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$n = - 6 (\frac{- 1}{4})$

Step 3.2.1.1.2

Factor $2$ out of $- 6$ .

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

Step 3.2.1.1.3

Factor $2$ out of $4$ .

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

Step 3.2.1.1.4

Cancel the common factor.

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

Step 3.2.1.1.5

Rewrite the expression.

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

Step 3.2.1.2

Combine $- 3$ and $\frac{- 1}{2}$ .

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

Step 3.2.1.3

Multiply $- 3$ by $- 1$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$n = 1.5$

Mixed Number Form:

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