Trigonometry Examples

$\frac{1}{2} \cdot (230 - x z) = 50$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (230 - x z)) = 2 \cdot 50$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $2 (\frac{1}{2} \cdot (230 - x z))$ .

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Step 2.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} \cdot 230 + \frac{1}{2} (- x z)) = 2 \cdot 50$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Factor $2$ out of $230$ .

$2 (\frac{1}{2} \cdot (2 (115)) + \frac{1}{2} (- x z)) = 2 \cdot 50$

Step 2.1.1.2.2

Cancel the common factor.

$2 (\frac{1}{2} \cdot (2 \cdot 115) + \frac{1}{2} (- x z)) = 2 \cdot 50$

Step 2.1.1.2.3

Rewrite the expression.

$2 (115 + \frac{1}{2} (- x z)) = 2 \cdot 50$

Step 2.1.1.3

Multiply $\frac{1}{2} (- x z)$ .

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Step 2.1.1.3.1

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

$2 (115 - \frac{x}{2} z) = 2 \cdot 50$

Step 2.1.1.3.2

Combine $z$ and $\frac{x}{2}$ .

$2 (115 - \frac{z x}{2}) = 2 \cdot 50$

Step 2.1.1.4

Apply the distributive property.

$2 \cdot 115 + 2 (- \frac{z x}{2}) = 2 \cdot 50$

Step 2.1.1.5

Multiply $2$ by $115$ .

$230 + 2 (- \frac{z x}{2}) = 2 \cdot 50$

Step 2.1.1.6

Cancel the common factor of $2$ .

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Step 2.1.1.6.1

Move the leading negative in $- \frac{z x}{2}$ into the numerator.

$230 + 2 \frac{- z x}{2} = 2 \cdot 50$

Step 2.1.1.6.2

Cancel the common factor.

$230 + 2 \frac{- z x}{2} = 2 \cdot 50$

Step 2.1.1.6.3

Rewrite the expression.

$230 - z x = 2 \cdot 50$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $50$ .

$230 - z x = 100$

Step 3

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

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Step 3.1

Subtract $230$ from both sides of the equation.

$- z x = 100 - 230$

Step 3.2

Subtract $230$ from $100$ .

$- z x = - 130$

Step 4

Divide each term in $- z x = - 130$ by $- z$ and simplify.

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Step 4.1

Divide each term in $- z x = - 130$ by $- z$ .

$\frac{- z x}{- z} = \frac{- 130}{- z}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{z x}{z} = \frac{- 130}{- z}$

Step 4.2.2

Cancel the common factor of $z$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{z x}{z} = \frac{- 130}{- z}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 130}{- z}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

$x = \frac{130}{z}$