Trigonometry Examples

$- \frac{1}{2} \cdot (4 x + 6) = \frac{1}{3} \cdot (9 - 3 x)$

Step 1

Simplify $- \frac{1}{2} \cdot (4 x + 6)$ .

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Step 1.1

Rewrite.

$0 + 0 - \frac{1}{2} \cdot (4 x + 6) = \frac{1}{3} \cdot (9 - 3 x)$

Step 1.2

Simplify by adding zeros.

$- \frac{1}{2} \cdot (4 x + 6) = \frac{1}{3} \cdot (9 - 3 x)$

Step 1.3

Apply the distributive property.

$- \frac{1}{2} (4 x) - \frac{1}{2} \cdot 6 = \frac{1}{3} \cdot (9 - 3 x)$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} (4 x) - \frac{1}{2} \cdot 6 = \frac{1}{3} \cdot (9 - 3 x)$

Step 1.4.2

Factor $2$ out of $4 x$ .

$\frac{- 1}{2} (2 (2 x)) - \frac{1}{2} \cdot 6 = \frac{1}{3} \cdot (9 - 3 x)$

Step 1.4.3

Cancel the common factor.

$\frac{- 1}{2} (2 (2 x)) - \frac{1}{2} \cdot 6 = \frac{1}{3} \cdot (9 - 3 x)$

Step 1.4.4

Rewrite the expression.

$- 1 (2 x) - \frac{1}{2} \cdot 6 = \frac{1}{3} \cdot (9 - 3 x)$

Step 1.5

Multiply $2$ by $- 1$ .

$- 2 x - \frac{1}{2} \cdot 6 = \frac{1}{3} \cdot (9 - 3 x)$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- 2 x + \frac{- 1}{2} \cdot 6 = \frac{1}{3} \cdot (9 - 3 x)$

Step 1.6.2

Factor $2$ out of $6$ .

$- 2 x + \frac{- 1}{2} \cdot (2 (3)) = \frac{1}{3} \cdot (9 - 3 x)$

Step 1.6.3

Cancel the common factor.

$- 2 x + \frac{- 1}{2} \cdot (2 \cdot 3) = \frac{1}{3} \cdot (9 - 3 x)$

Step 1.6.4

Rewrite the expression.

$- 2 x - 1 \cdot 3 = \frac{1}{3} \cdot (9 - 3 x)$

Step 1.7

Multiply $- 1$ by $3$ .

$- 2 x - 3 = \frac{1}{3} \cdot (9 - 3 x)$

Step 2

Simplify $\frac{1}{3} \cdot (9 - 3 x)$ .

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Step 2.1

Apply the distributive property.

$- 2 x - 3 = \frac{1}{3} \cdot 9 + \frac{1}{3} (- 3 x)$

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Factor $3$ out of $9$ .

$- 2 x - 3 = \frac{1}{3} \cdot (3 (3)) + \frac{1}{3} (- 3 x)$

Step 2.2.2

Cancel the common factor.

$- 2 x - 3 = \frac{1}{3} \cdot (3 \cdot 3) + \frac{1}{3} (- 3 x)$

Step 2.2.3

Rewrite the expression.

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

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Factor $3$ out of $- 3 x$ .

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

Step 2.3.2

Cancel the common factor.

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

Step 2.3.3

Rewrite the expression.

$- 2 x - 3 = 3 - x$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Add $x$ to both sides of the equation.

$- 2 x - 3 + x = 3$

Step 3.2

Add $- 2 x$ and $x$ .

$- x - 3 = 3$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$- x = 3 + 3$

Step 4.2

Add $3$ and $3$ .

$- x = 6$

Step 5

Divide each term in $- x = 6$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- x = 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{6}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{6}{- 1}$

Step 5.2.2

Divide $x$ by $1$ .

$x = \frac{6}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $6$ by $- 1$ .

$x = - 6$