Algebra Examples

$8 - | 2 + 2 x | = 0$

Step 1

Subtract $8$ from both sides of the equation.

$- | 2 + 2 x | = - 8$

Step 2

Divide each term in $- | 2 + 2 x | = - 8$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- | 2 + 2 x | = - 8$ by $- 1$ .

$\frac{- | 2 + 2 x |}{- 1} = \frac{- 8}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{| 2 + 2 x |}{1} = \frac{- 8}{- 1}$

Step 2.2.2

Divide $| 2 + 2 x |$ by $1$ .

$| 2 + 2 x | = \frac{- 8}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 8$ by $- 1$ .

$| 2 + 2 x | = 8$

Step 3

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

$2 + 2 x = \pm 8$

Step 4

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

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Step 4.1

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

$2 + 2 x = 8$

Step 4.2

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

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Step 4.2.1

Subtract $2$ from both sides of the equation.

$2 x = 8 - 2$

Step 4.2.2

Subtract $2$ from $8$ .

$2 x = 6$

Step 4.3

Divide each term in $2 x = 6$ by $2$ and simplify.

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Step 4.3.1

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $2$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $6$ by $2$ .

$x = 3$

Step 4.4

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

$2 + 2 x = - 8$

Step 4.5

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

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Step 4.5.1

Subtract $2$ from both sides of the equation.

$2 x = - 8 - 2$

Step 4.5.2

Subtract $2$ from $- 8$ .

$2 x = - 10$

Step 4.6

Divide each term in $2 x = - 10$ by $2$ and simplify.

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Step 4.6.1

Divide each term in $2 x = - 10$ by $2$ .

$\frac{2 x}{2} = \frac{- 10}{2}$

Step 4.6.2

Simplify the left side.

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Step 4.6.2.1

Cancel the common factor of $2$ .

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Step 4.6.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 10}{2}$

Step 4.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 10}{2}$

Step 4.6.3

Simplify the right side.

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Step 4.6.3.1

Divide $- 10$ by $2$ .

$x = - 5$

Step 4.7

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

$x = 3, - 5$