Finite Math Examples

$| 2 x | = 8$ , $0.4$

Step 1

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

$2 x = \pm 8$

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.

$2 x = 8$

Step 2.2

Divide each term in $2 x = 8$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 x = 8$ by $2$ .

$\frac{2 x}{2} = \frac{8}{2}$

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.

$\frac{2 x}{2} = \frac{8}{2}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $8$ by $2$ .

$x = 4$

Step 2.3

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

$2 x = - 8$

Step 2.4

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

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Step 2.4.1

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

$\frac{2 x}{2} = \frac{- 8}{2}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $2$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 8}{2}$

Step 2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{2}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $- 8$ by $2$ .

$x = - 4$

Step 2.5

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

$x = 4, - 4$

Step 3

Replace the variable $x$ with $4$ in the expression.

$0.4$