Trigonometry Examples

$55 - (x + 10) = - 2 (\frac{1}{2} + 10)$

Step 1

Simplify $55 - (x + 10)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$55 - x - 1 \cdot 10 = - 2 (\frac{1}{2} + 10)$

Step 1.1.2

Multiply $- 1$ by $10$ .

$55 - x - 10 = - 2 (\frac{1}{2} + 10)$

Step 1.2

Subtract $10$ from $55$ .

$- x + 45 = - 2 (\frac{1}{2} + 10)$

Step 2

Simplify $- 2 (\frac{1}{2} + 10)$ .

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Step 2.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- x + 45 = - 2 (\frac{1}{2} + 10 \cdot \frac{2}{2})$

Step 2.2

Combine $10$ and $\frac{2}{2}$ .

$- x + 45 = - 2 (\frac{1}{2} + \frac{10 \cdot 2}{2})$

Step 2.3

Combine the numerators over the common denominator.

$- x + 45 = - 2 \frac{1 + 10 \cdot 2}{2}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $10$ by $2$ .

$- x + 45 = - 2 \frac{1 + 20}{2}$

Step 2.4.2

Add $1$ and $20$ .

$- x + 45 = - 2 (\frac{21}{2})$

Step 2.5

Cancel the common factor of $2$ .

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Step 2.5.1

Factor $2$ out of $- 2$ .

$- x + 45 = 2 (- 1) \frac{21}{2}$

Step 2.5.2

Cancel the common factor.

$- x + 45 = 2 \cdot - 1 \frac{21}{2}$

Step 2.5.3

Rewrite the expression.

$- x + 45 = - 1 \cdot 21$

Step 2.6

Multiply $- 1$ by $21$ .

$- x + 45 = - 21$

Step 3

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

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Step 3.1

Subtract $45$ from both sides of the equation.

$- x = - 21 - 45$

Step 3.2

Subtract $45$ from $- 21$ .

$- x = - 66$

Step 4

Divide each term in $- x = - 66$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- x = - 66$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 66}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 66}{- 1}$

Step 4.2.2

Divide $x$ by $1$ .

$x = \frac{- 66}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 66$ by $- 1$ .

$x = 66$