Trigonometry Examples

$1 - \frac{3}{4} \cdot (v - 2) = - 5$

Step 1

Add $5$ to both sides of the equation.

$1 - \frac{3}{4} \cdot (v - 2) + 5 = 0$

Step 2

Simplify $1 - \frac{3}{4} \cdot (v - 2) + 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$1 - \frac{3}{4} v - \frac{3}{4} \cdot - 2 + 5 = 0$

Step 2.1.2

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

$1 - \frac{v \cdot 3}{4} - \frac{3}{4} \cdot - 2 + 5 = 0$

Step 2.1.3

Cancel the common factor of $2$ .

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Step 2.1.3.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$1 - \frac{v \cdot 3}{4} + \frac{- 3}{4} \cdot - 2 + 5 = 0$

Step 2.1.3.2

Factor $2$ out of $4$ .

$1 - \frac{v \cdot 3}{4} + \frac{- 3}{2 (2)} \cdot - 2 + 5 = 0$

Step 2.1.3.3

Factor $2$ out of $- 2$ .

$1 - \frac{v \cdot 3}{4} + \frac{- 3}{2 \cdot 2} \cdot (2 \cdot - 1) + 5 = 0$

Step 2.1.3.4

Cancel the common factor.

$1 - \frac{v \cdot 3}{4} + \frac{- 3}{2 \cdot 2} \cdot (2 \cdot - 1) + 5 = 0$

Step 2.1.3.5

Rewrite the expression.

$1 - \frac{v \cdot 3}{4} + \frac{- 3}{2} \cdot - 1 + 5 = 0$

Step 2.1.4

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

$1 - \frac{v \cdot 3}{4} + \frac{- 3 \cdot - 1}{2} + 5 = 0$

Step 2.1.5

Multiply $- 3$ by $- 1$ .

$1 - \frac{v \cdot 3}{4} + \frac{3}{2} + 5 = 0$

Step 2.1.6

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

$1 - \frac{3 v}{4} + \frac{3}{2} + 5 = 0$

Step 2.2

Write $1$ as a fraction with a common denominator.

$- \frac{3 v}{4} + \frac{2}{2} + \frac{3}{2} + 5 = 0$

Step 2.3

Combine the numerators over the common denominator.

$- \frac{3 v}{4} + \frac{2 + 3}{2} + 5 = 0$

Step 2.4

Add $2$ and $3$ .

$- \frac{3 v}{4} + \frac{5}{2} + 5 = 0$

Step 2.5

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 v}{4} + \frac{5}{2} + 5 \cdot \frac{2}{2} = 0$

Step 2.6

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

$- \frac{3 v}{4} + \frac{5}{2} + \frac{5 \cdot 2}{2} = 0$

Step 2.7

Combine the numerators over the common denominator.

$- \frac{3 v}{4} + \frac{5 + 5 \cdot 2}{2} = 0$

Step 2.8

Simplify the numerator.

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Step 2.8.1

Multiply $5$ by $2$ .

$- \frac{3 v}{4} + \frac{5 + 10}{2} = 0$

Step 2.8.2

Add $5$ and $10$ .

$- \frac{3 v}{4} + \frac{15}{2} = 0$

Step 3

Factor the left side.

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Step 3.1

To write $\frac{15}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 v}{4} + \frac{15}{2} \cdot \frac{2}{2} = 0$

Step 3.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1

Multiply $\frac{15}{2}$ by $\frac{2}{2}$ .

$- \frac{3 v}{4} + \frac{15 \cdot 2}{2 \cdot 2} = 0$

Step 3.2.2

Multiply $2$ by $2$ .

$- \frac{3 v}{4} + \frac{15 \cdot 2}{4} = 0$

Step 3.3

Combine the numerators over the common denominator.

$\frac{- 3 v + 15 \cdot 2}{4} = 0$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Factor $3$ out of $- 3 v + 15 \cdot 2$ .

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Step 3.4.1.1

Factor $3$ out of $- 3 v$ .

$\frac{3 (- v) + 15 \cdot 2}{4} = 0$

Step 3.4.1.2

Factor $3$ out of $15 \cdot 2$ .

$\frac{3 (- v) + 3 (5 \cdot 2)}{4} = 0$

Step 3.4.1.3

Factor $3$ out of $3 (- v) + 3 (5 \cdot 2)$ .

$\frac{3 (- v + 5 \cdot 2)}{4} = 0$

Step 3.4.2

Multiply $5$ by $2$ .

$\frac{3 (- v + 10)}{4} = 0$