Trigonometry Examples

$x (\frac{2}{3}) - 7 x \frac{1}{3} + 6 = 0$

Step 1

Simplify $x (\frac{2}{3}) - 7 x \frac{1}{3} + 6$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $x$ and $\frac{2}{3}$ .

$\frac{x \cdot 2}{3} - 7 x \frac{1}{3} + 6 = 0$

Step 1.1.2

Move $2$ to the left of $x$ .

$\frac{2 \cdot x}{3} - 7 x \frac{1}{3} + 6 = 0$

Step 1.1.3

Multiply $- 7 x \frac{1}{3}$ .

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Step 1.1.3.1

Combine $- 7$ and $\frac{1}{3}$ .

$\frac{2 x}{3} + x \frac{- 7}{3} + 6 = 0$

Step 1.1.3.2

Combine $x$ and $\frac{- 7}{3}$ .

$\frac{2 x}{3} + \frac{x \cdot - 7}{3} + 6 = 0$

Step 1.1.4

Move $- 7$ to the left of $x$ .

$\frac{2 x}{3} + \frac{- 7 \cdot x}{3} + 6 = 0$

Step 1.1.5

Move the negative in front of the fraction.

$\frac{2 x}{3} - \frac{7 x}{3} + 6 = 0$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$6 + \frac{2 x - 7 x}{3} = 0$

Step 1.2.2

Subtract $7 x$ from $2 x$ .

$6 + \frac{- 5 x}{3} = 0$

Step 1.2.3

Move the negative in front of the fraction.

$6 - \frac{5 x}{3} = 0$

Step 2

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

$x = \frac{18}{5}$

Step 3