Pre-Algebra Examples

$2 | 2 x - 1 | - 8 = 18$

Step 1

Move all terms not containing $| 2 x - 1 |$ to the right side of the equation.

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Step 1.1

Add $8$ to both sides of the equation.

$2 | 2 x - 1 | = 18 + 8$

Step 1.2

Add $18$ and $8$ .

$2 | 2 x - 1 | = 26$

Step 2

Divide each term in $2 | 2 x - 1 | = 26$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 | 2 x - 1 | = 26$ by $2$ .

$\frac{2 | 2 x - 1 |}{2} = \frac{26}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 | 2 x - 1 |}{2} = \frac{26}{2}$

Step 2.2.1.2

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

$| 2 x - 1 | = \frac{26}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $26$ by $2$ .

$| 2 x - 1 | = 13$

Step 3

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

$2 x - 1 = \pm 13$

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.

$2 x - 1 = 13$

Step 4.2

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

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Step 4.2.1

Add $1$ to both sides of the equation.

$2 x = 13 + 1$

Step 4.2.2

Add $13$ and $1$ .

$2 x = 14$

Step 4.3

Divide each term in $2 x = 14$ by $2$ and simplify.

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Step 4.3.1

Divide each term in $2 x = 14$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2}$

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.

$\frac{2 x}{2} = \frac{14}{2}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{14}{2}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $14$ by $2$ .

$x = 7$

Step 4.4

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

$2 x - 1 = - 13$

Step 4.5

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

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Step 4.5.1

Add $1$ to both sides of the equation.

$2 x = - 13 + 1$

Step 4.5.2

Add $- 13$ and $1$ .

$2 x = - 12$

Step 4.6

Divide each term in $2 x = - 12$ by $2$ and simplify.

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Step 4.6.1

Divide each term in $2 x = - 12$ by $2$ .

$\frac{2 x}{2} = \frac{- 12}{2}$

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.

$\frac{2 x}{2} = \frac{- 12}{2}$

Step 4.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{2}$

Step 4.6.3

Simplify the right side.

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Step 4.6.3.1

Divide $- 12$ by $2$ .

$x = - 6$

Step 4.7

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

$x = 7, - 6$