Trigonometry Examples

$\frac{2 x - 1}{3} - \frac{3}{4} - \frac{6 x + 1}{12} = - \frac{2}{3}$

Step 1

Simplify $\frac{2 x - 1}{3} - \frac{3}{4} - \frac{6 x + 1}{12}$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Multiply $\frac{2 x - 1}{3}$ by $\frac{4}{4}$ .

$\frac{2 x - 1}{3} \cdot \frac{4}{4} - \frac{3}{4} - \frac{6 x + 1}{12} = - \frac{2}{3}$

Step 1.1.2

Multiply $\frac{2 x - 1}{3}$ by $\frac{4}{4}$ .

$\frac{(2 x - 1) \cdot 4}{3 \cdot 4} - \frac{3}{4} - \frac{6 x + 1}{12} = - \frac{2}{3}$

Step 1.1.3

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$\frac{(2 x - 1) \cdot 4}{3 \cdot 4} - (\frac{3}{4} \cdot \frac{3}{3}) - \frac{6 x + 1}{12} = - \frac{2}{3}$

Step 1.1.4

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$\frac{(2 x - 1) \cdot 4}{3 \cdot 4} - \frac{3 \cdot 3}{4 \cdot 3} - \frac{6 x + 1}{12} = - \frac{2}{3}$

Step 1.1.5

Multiply $3$ by $4$ .

$\frac{(2 x - 1) \cdot 4}{12} - \frac{3 \cdot 3}{4 \cdot 3} - \frac{6 x + 1}{12} = - \frac{2}{3}$

Step 1.1.6

Reorder the factors of $4 \cdot 3$ .

$\frac{(2 x - 1) \cdot 4}{12} - \frac{3 \cdot 3}{3 \cdot 4} - \frac{6 x + 1}{12} = - \frac{2}{3}$

Step 1.1.7

Multiply $3$ by $4$ .

$\frac{(2 x - 1) \cdot 4}{12} - \frac{3 \cdot 3}{12} - \frac{6 x + 1}{12} = - \frac{2}{3}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{(2 x - 1) \cdot 4 - 3 \cdot 3 - (6 x + 1)}{12} = - \frac{2}{3}$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$\frac{2 x \cdot 4 - 1 \cdot 4 - 3 \cdot 3 - (6 x + 1)}{12} = - \frac{2}{3}$

Step 1.3.2

Multiply $4$ by $2$ .

$\frac{8 x - 1 \cdot 4 - 3 \cdot 3 - (6 x + 1)}{12} = - \frac{2}{3}$

Step 1.3.3

Multiply $- 1$ by $4$ .

$\frac{8 x - 4 - 3 \cdot 3 - (6 x + 1)}{12} = - \frac{2}{3}$

Step 1.3.4

Multiply $- 3$ by $3$ .

$\frac{8 x - 4 - 9 - (6 x + 1)}{12} = - \frac{2}{3}$

Step 1.3.5

Apply the distributive property.

$\frac{8 x - 4 - 9 - (6 x) - 1 \cdot 1}{12} = - \frac{2}{3}$

Step 1.3.6

Multiply $6$ by $- 1$ .

$\frac{8 x - 4 - 9 - 6 x - 1 \cdot 1}{12} = - \frac{2}{3}$

Step 1.3.7

Multiply $- 1$ by $1$ .

$\frac{8 x - 4 - 9 - 6 x - 1}{12} = - \frac{2}{3}$

Step 1.4

Simplify terms.

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Step 1.4.1

Subtract $6 x$ from $8 x$ .

$\frac{2 x - 4 - 9 - 1}{12} = - \frac{2}{3}$

Step 1.4.2

Simplify by subtracting numbers.

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Step 1.4.2.1

Subtract $9$ from $- 4$ .

$\frac{2 x - 13 - 1}{12} = - \frac{2}{3}$

Step 1.4.2.2

Subtract $1$ from $- 13$ .

$\frac{2 x - 14}{12} = - \frac{2}{3}$

Step 1.4.3

Cancel the common factor of $2 x - 14$ and $12$ .

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Step 1.4.3.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) - 14}{12} = - \frac{2}{3}$

Step 1.4.3.2

Factor $2$ out of $- 14$ .

$\frac{2 x + 2 \cdot - 7}{12} = - \frac{2}{3}$

Step 1.4.3.3

Factor $2$ out of $2 x + 2 \cdot - 7$ .

$\frac{2 (x - 7)}{12} = - \frac{2}{3}$

Step 1.4.3.4

Cancel the common factors.

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Step 1.4.3.4.1

Factor $2$ out of $12$ .

$\frac{2 (x - 7)}{2 (6)} = - \frac{2}{3}$

Step 1.4.3.4.2

Cancel the common factor.

$\frac{2 (x - 7)}{2 \cdot 6} = - \frac{2}{3}$

Step 1.4.3.4.3

Rewrite the expression.

$\frac{x - 7}{6} = - \frac{2}{3}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 3$

Step 3