Algebra Examples

$| 6 - 3 c | = 14$

Step 1

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

$6 - 3 c = \pm 14$

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.

$6 - 3 c = 14$

Step 2.2

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

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Step 2.2.1

Subtract $6$ from both sides of the equation.

$- 3 c = 14 - 6$

Step 2.2.2

Subtract $6$ from $14$ .

$- 3 c = 8$

Step 2.3

Divide each term in $- 3 c = 8$ by $- 3$ and simplify.

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Step 2.3.1

Divide each term in $- 3 c = 8$ by $- 3$ .

$\frac{- 3 c}{- 3} = \frac{8}{- 3}$

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.

$\frac{- 3 c}{- 3} = \frac{8}{- 3}$

Step 2.3.2.1.2

Divide $c$ by $1$ .

$c = \frac{8}{- 3}$

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.

$c = - \frac{8}{3}$

Step 2.4

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

$6 - 3 c = - 14$

Step 2.5

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

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Step 2.5.1

Subtract $6$ from both sides of the equation.

$- 3 c = - 14 - 6$

Step 2.5.2

Subtract $6$ from $- 14$ .

$- 3 c = - 20$

Step 2.6

Divide each term in $- 3 c = - 20$ by $- 3$ and simplify.

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Step 2.6.1

Divide each term in $- 3 c = - 20$ by $- 3$ .

$\frac{- 3 c}{- 3} = \frac{- 20}{- 3}$

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.

$\frac{- 3 c}{- 3} = \frac{- 20}{- 3}$

Step 2.6.2.1.2

Divide $c$ by $1$ .

$c = \frac{- 20}{- 3}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Dividing two negative values results in a positive value.

$c = \frac{20}{3}$

Step 2.7

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

$c = - \frac{8}{3}, \frac{20}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$c = - \frac{8}{3}, \frac{20}{3}$

Decimal Form:

$c = - 2.\overline{6}, 6.\overline{6}$

Mixed Number Form:

$c = - 2 \frac{2}{3}, 6 \frac{2}{3}$