Finite Math Examples

$10 - | 8 - x | = - 6$

Step 1

Move all terms not containing $| 8 - x |$ to the right side of the equation.

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Step 1.1

Subtract $10$ from both sides of the equation.

$- | 8 - x | = - 6 - 10$

Step 1.2

Subtract $10$ from $- 6$ .

$- | 8 - x | = - 16$

Step 2

Divide each term in $- | 8 - x | = - 16$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- | 8 - x | = - 16$ by $- 1$ .

$\frac{- | 8 - x |}{- 1} = \frac{- 16}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{| 8 - x |}{1} = \frac{- 16}{- 1}$

Step 2.2.2

Divide $| 8 - x |$ by $1$ .

$| 8 - x | = \frac{- 16}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 16$ by $- 1$ .

$| 8 - x | = 16$

Step 3

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

$8 - x = \pm 16$

Step 4

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

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Step 4.1

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

$8 - x = 16$

Step 4.2

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

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Step 4.2.1

Subtract $8$ from both sides of the equation.

$- x = 16 - 8$

Step 4.2.2

Subtract $8$ from $16$ .

$- x = 8$

Step 4.3

Divide each term in $- x = 8$ by $- 1$ and simplify.

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Step 4.3.1

Divide each term in $- x = 8$ by $- 1$ .

$\frac{- x}{- 1} = \frac{8}{- 1}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{8}{- 1}$

Step 4.3.2.2

Divide $x$ by $1$ .

$x = \frac{8}{- 1}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $8$ by $- 1$ .

$x = - 8$

Step 4.4

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

$8 - x = - 16$

Step 4.5

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

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Step 4.5.1

Subtract $8$ from both sides of the equation.

$- x = - 16 - 8$

Step 4.5.2

Subtract $8$ from $- 16$ .

$- x = - 24$

Step 4.6

Divide each term in $- x = - 24$ by $- 1$ and simplify.

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Step 4.6.1

Divide each term in $- x = - 24$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 24}{- 1}$

Step 4.6.2

Simplify the left side.

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Step 4.6.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 24}{- 1}$

Step 4.6.2.2

Divide $x$ by $1$ .

$x = \frac{- 24}{- 1}$

Step 4.6.3

Simplify the right side.

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Step 4.6.3.1

Divide $- 24$ by $- 1$ .

$x = 24$

Step 4.7

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

$x = - 8, 24$