Finite Math Examples

$| 6 x | - 8 = 28$

Step 1

Move all terms not containing $| 6 x |$ to the right side of the equation.

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Step 1.1

Add $8$ to both sides of the equation.

$| 6 x | = 28 + 8$

Step 1.2

Add $28$ and $8$ .

$| 6 x | = 36$

Step 2

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

$6 x = \pm 36$

Step 3

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

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Step 3.1

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

$6 x = 36$

Step 3.2

Divide each term in $6 x = 36$ by $6$ and simplify.

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Step 3.2.1

Divide each term in $6 x = 36$ by $6$ .

$\frac{6 x}{6} = \frac{36}{6}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $6$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{36}{6}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{36}{6}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $36$ by $6$ .

$x = 6$

Step 3.3

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

$6 x = - 36$

Step 3.4

Divide each term in $6 x = - 36$ by $6$ and simplify.

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Step 3.4.1

Divide each term in $6 x = - 36$ by $6$ .

$\frac{6 x}{6} = \frac{- 36}{6}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $6$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 36}{6}$

Step 3.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 36}{6}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $- 36$ by $6$ .

$x = - 6$

Step 3.5

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

$x = 6, - 6$