Finite Math Examples

$| x + \frac{2}{5} | = \frac{22}{5}$

Step 1

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

$x + \frac{2}{5} = \pm \frac{22}{5}$

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.

$x + \frac{2}{5} = \frac{22}{5}$

Step 2.2

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

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Step 2.2.1

Subtract $\frac{2}{5}$ from both sides of the equation.

$x = \frac{22}{5} - \frac{2}{5}$

Step 2.2.2

Combine the numerators over the common denominator.

$x = \frac{22 - 2}{5}$

Step 2.2.3

Subtract $2$ from $22$ .

$x = \frac{20}{5}$

Step 2.2.4

Divide $20$ by $5$ .

$x = 4$

Step 2.3

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

$x + \frac{2}{5} = - \frac{22}{5}$

Step 2.4

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

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Step 2.4.1

Subtract $\frac{2}{5}$ from both sides of the equation.

$x = - \frac{22}{5} - \frac{2}{5}$

Step 2.4.2

Combine the numerators over the common denominator.

$x = \frac{- 22 - 2}{5}$

Step 2.4.3

Subtract $2$ from $- 22$ .

$x = \frac{- 24}{5}$

Step 2.4.4

Move the negative in front of the fraction.

$x = - \frac{24}{5}$

Step 2.5

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

$x = 4, - \frac{24}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = 4, - \frac{24}{5}$

Decimal Form:

$x = 4, - 4.8$

Mixed Number Form:

$x = 4, - 4 \frac{4}{5}$