Algebra Examples

$| 2 (x - 1) | = 11$

Step 1

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

$2 (x - 1) = \pm 11$

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.

$2 (x - 1) = 11$

Step 2.2

Divide each term in $2 (x - 1) = 11$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 (x - 1) = 11$ by $2$ .

$\frac{2 (x - 1)}{2} = \frac{11}{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 (x - 1)}{2} = \frac{11}{2}$

Step 2.2.2.1.2

Divide $x - 1$ by $1$ .

$x - 1 = \frac{11}{2}$

Step 2.3

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

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Step 2.3.1

Add $1$ to both sides of the equation.

$x = \frac{11}{2} + 1$

Step 2.3.2

Write $1$ as a fraction with a common denominator.

$x = \frac{11}{2} + \frac{2}{2}$

Step 2.3.3

Combine the numerators over the common denominator.

$x = \frac{11 + 2}{2}$

Step 2.3.4

Add $11$ and $2$ .

$x = \frac{13}{2}$

Step 2.4

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

$2 (x - 1) = - 11$

Step 2.5

Divide each term in $2 (x - 1) = - 11$ by $2$ and simplify.

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Step 2.5.1

Divide each term in $2 (x - 1) = - 11$ by $2$ .

$\frac{2 (x - 1)}{2} = \frac{- 11}{2}$

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Cancel the common factor of $2$ .

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Step 2.5.2.1.1

Cancel the common factor.

$\frac{2 (x - 1)}{2} = \frac{- 11}{2}$

Step 2.5.2.1.2

Divide $x - 1$ by $1$ .

$x - 1 = \frac{- 11}{2}$

Step 2.5.3

Simplify the right side.

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Step 2.5.3.1

Move the negative in front of the fraction.

$x - 1 = - \frac{11}{2}$

Step 2.6

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

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Step 2.6.1

Add $1$ to both sides of the equation.

$x = - \frac{11}{2} + 1$

Step 2.6.2

Write $1$ as a fraction with a common denominator.

$x = - \frac{11}{2} + \frac{2}{2}$

Step 2.6.3

Combine the numerators over the common denominator.

$x = \frac{- 11 + 2}{2}$

Step 2.6.4

Add $- 11$ and $2$ .

$x = \frac{- 9}{2}$

Step 2.6.5

Move the negative in front of the fraction.

$x = - \frac{9}{2}$

Step 2.7

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

$x = \frac{13}{2}, - \frac{9}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13}{2}, - \frac{9}{2}$

Decimal Form:

$x = 6.5, - 4.5$

Mixed Number Form:

$x = 6 \frac{1}{2}, - 4 \frac{1}{2}$