Trigonometry Examples

$| 6 - 2 x | + 3 x = 4 x + 12$

Step 1

Move all terms not containing $| 6 - 2 x |$ to the right side of the equation.

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Step 1.1

Subtract $3 x$ from both sides of the equation.

$| 6 - 2 x | = 4 x + 12 - 3 x$

Step 1.2

Subtract $3 x$ from $4 x$ .

$| 6 - 2 x | = x + 12$

Step 2

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

$6 - 2 x = \pm (x + 12)$

Step 3

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

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Step 3.1

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

$6 - 2 x = x + 12$

Step 3.2

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

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Step 3.2.1

Subtract $x$ from both sides of the equation.

$6 - 2 x - x = 12$

Step 3.2.2

Subtract $x$ from $- 2 x$ .

$6 - 3 x = 12$

Step 3.3

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

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Step 3.3.1

Subtract $6$ from both sides of the equation.

$- 3 x = 12 - 6$

Step 3.3.2

Subtract $6$ from $12$ .

$- 3 x = 6$

Step 3.4

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

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Step 3.4.1

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

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

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $- 3$ .

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Step 3.4.2.1.1

Cancel the common factor.

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

Step 3.4.2.1.2

Divide $x$ by $1$ .

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

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $6$ by $- 3$ .

$x = - 2$

Step 3.5

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

$6 - 2 x = - (x + 12)$

Step 3.6

Simplify $- (x + 12)$ .

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Step 3.6.1

Rewrite.

$6 - 2 x = 0 + 0 - (x + 12)$

Step 3.6.2

Simplify by adding zeros.

$6 - 2 x = - (x + 12)$

Step 3.6.3

Apply the distributive property.

$6 - 2 x = - x - 1 \cdot 12$

Step 3.6.4

Multiply $- 1$ by $12$ .

$6 - 2 x = - x - 12$

Step 3.7

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

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Step 3.7.1

Add $x$ to both sides of the equation.

$6 - 2 x + x = - 12$

Step 3.7.2

Add $- 2 x$ and $x$ .

$6 - x = - 12$

Step 3.8

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

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Step 3.8.1

Subtract $6$ from both sides of the equation.

$- x = - 12 - 6$

Step 3.8.2

Subtract $6$ from $- 12$ .

$- x = - 18$

Step 3.9

Divide each term in $- x = - 18$ by $- 1$ and simplify.

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Step 3.9.1

Divide each term in $- x = - 18$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 18}{- 1}$

Step 3.9.2

Simplify the left side.

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Step 3.9.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 18}{- 1}$

Step 3.9.2.2

Divide $x$ by $1$ .

$x = \frac{- 18}{- 1}$

Step 3.9.3

Simplify the right side.

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Step 3.9.3.1

Divide $- 18$ by $- 1$ .

$x = 18$

Step 3.10

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

$x = - 2, 18$