Trigonometry Examples

$2 a + 2 b + 2 d = 164$

Step 1

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

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Step 1.1

Subtract $2 b$ from both sides of the equation.

$2 a + 2 d = 164 - 2 b$

Step 1.2

Subtract $2 d$ from both sides of the equation.

$2 a = 164 - 2 b - 2 d$

Step 2

Divide each term in $2 a = 164 - 2 b - 2 d$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 a = 164 - 2 b - 2 d$ by $2$ .

$\frac{2 a}{2} = \frac{164}{2} + \frac{- 2 b}{2} + \frac{- 2 d}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{164}{2} + \frac{- 2 b}{2} + \frac{- 2 d}{2}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a = \frac{164}{2} + \frac{- 2 b}{2} + \frac{- 2 d}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $164$ by $2$ .

$a = 82 + \frac{- 2 b}{2} + \frac{- 2 d}{2}$

Step 2.3.1.2

Cancel the common factor of $- 2$ and $2$ .

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Step 2.3.1.2.1

Factor $2$ out of $- 2 b$ .

$a = 82 + \frac{2 (- b)}{2} + \frac{- 2 d}{2}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $2$ out of $2$ .

$a = 82 + \frac{2 (- b)}{2 (1)} + \frac{- 2 d}{2}$

Step 2.3.1.2.2.2

Cancel the common factor.

$a = 82 + \frac{2 (- b)}{2 \cdot 1} + \frac{- 2 d}{2}$

Step 2.3.1.2.2.3

Rewrite the expression.

$a = 82 + \frac{- b}{1} + \frac{- 2 d}{2}$

Step 2.3.1.2.2.4

Divide $- b$ by $1$ .

$a = 82 - b + \frac{- 2 d}{2}$

Step 2.3.1.3

Cancel the common factor of $- 2$ and $2$ .

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Step 2.3.1.3.1

Factor $2$ out of $- 2 d$ .

$a = 82 - b + \frac{2 (- d)}{2}$

Step 2.3.1.3.2

Cancel the common factors.

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Step 2.3.1.3.2.1

Factor $2$ out of $2$ .

$a = 82 - b + \frac{2 (- d)}{2 (1)}$

Step 2.3.1.3.2.2

Cancel the common factor.

$a = 82 - b + \frac{2 (- d)}{2 \cdot 1}$

Step 2.3.1.3.2.3

Rewrite the expression.

$a = 82 - b + \frac{- d}{1}$

Step 2.3.1.3.2.4

Divide $- d$ by $1$ .

$a = 82 - b - d$