Finite Math Examples

$5 + | 6 n | = 35$

Step 1

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

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Step 1.1

Subtract $5$ from both sides of the equation.

$| 6 n | = 35 - 5$

Step 1.2

Subtract $5$ from $35$ .

$| 6 n | = 30$

Step 2

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

$6 n = \pm 30$

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.

$6 n = 30$

Step 3.2

Divide each term in $6 n = 30$ by $6$ and simplify.

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Step 3.2.1

Divide each term in $6 n = 30$ by $6$ .

$\frac{6 n}{6} = \frac{30}{6}$

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.

$\frac{6 n}{6} = \frac{30}{6}$

Step 3.2.2.1.2

Divide $n$ by $1$ .

$n = \frac{30}{6}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $30$ by $6$ .

$n = 5$

Step 3.3

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

$6 n = - 30$

Step 3.4

Divide each term in $6 n = - 30$ by $6$ and simplify.

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Step 3.4.1

Divide each term in $6 n = - 30$ by $6$ .

$\frac{6 n}{6} = \frac{- 30}{6}$

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.

$\frac{6 n}{6} = \frac{- 30}{6}$

Step 3.4.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 30}{6}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $- 30$ by $6$ .

$n = - 5$

Step 3.5

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

$n = 5, - 5$