Trigonometry Examples

$| 2 - 3 x | = 4$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$2 - 3 x = \pm 4$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$2 - 3 x = 4$

Step 2.2

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

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Step 2.2.1

Subtract $2$ from both sides of the equation.

$- 3 x = 4 - 2$

Step 2.2.2

Subtract $2$ from $4$ .

$- 3 x = 2$

Step 2.3

Divide each term in $- 3 x = 2$ by $- 3$ and simplify.

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Step 2.3.1

Divide each term in $- 3 x = 2$ by $- 3$ .

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 3$ .

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Step 2.3.2.1.1

Cancel the common factor.

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

Step 2.3.2.1.2

Divide $x$ by $1$ .

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

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Move the negative in front of the fraction.

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

Step 2.4

Next, use the negative value of the $\pm$ to find the second solution.

$2 - 3 x = - 4$

Step 2.5

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

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Step 2.5.1

Subtract $2$ from both sides of the equation.

$- 3 x = - 4 - 2$

Step 2.5.2

Subtract $2$ from $- 4$ .

$- 3 x = - 6$

Step 2.6

Divide each term in $- 3 x = - 6$ by $- 3$ and simplify.

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Step 2.6.1

Divide each term in $- 3 x = - 6$ by $- 3$ .

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

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of $- 3$ .

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Step 2.6.2.1.1

Cancel the common factor.

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

Step 2.6.2.1.2

Divide $x$ by $1$ .

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

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Divide $- 6$ by $- 3$ .

$x = 2$

Step 2.7

The complete solution is the result of both the positive and negative portions of the solution.

$x = - \frac{2}{3}, 2$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{2}{3}, 2$

Decimal Form:

$x = - 0.\overline{6}, 2$