Pre-Algebra Examples

$9 - | 9 x | = 8$

Step 1

Move all terms not containing $| 9 x |$ to the right side of the equation.

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Step 1.1

Subtract $9$ from both sides of the equation.

$- | 9 x | = 8 - 9$

Step 1.2

Subtract $9$ from $8$ .

$- | 9 x | = - 1$

Step 2

Divide each term in $- | 9 x | = - 1$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- | 9 x | = - 1$ by $- 1$ .

$\frac{- | 9 x |}{- 1} = \frac{- 1}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{| 9 x |}{1} = \frac{- 1}{- 1}$

Step 2.2.2

Divide $| 9 x |$ by $1$ .

$| 9 x | = \frac{- 1}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 1$ by $- 1$ .

$| 9 x | = 1$

Step 3

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

$9 x = \pm 1$

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.

$9 x = 1$

Step 4.2

Divide each term in $9 x = 1$ by $9$ and simplify.

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Step 4.2.1

Divide each term in $9 x = 1$ by $9$ .

$\frac{9 x}{9} = \frac{1}{9}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $9$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{1}{9}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{9}$

Step 4.3

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

$9 x = - 1$

Step 4.4

Divide each term in $9 x = - 1$ by $9$ and simplify.

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Step 4.4.1

Divide each term in $9 x = - 1$ by $9$ .

$\frac{9 x}{9} = \frac{- 1}{9}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $9$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{- 1}{9}$

Step 4.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{9}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{9}$

Step 4.5

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

$x = \frac{1}{9}, - \frac{1}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{9}, - \frac{1}{9}$

Decimal Form:

$x = 0.\overline{1}, - 0.\overline{1}$