Basic Math Examples

$| \frac{2 s - 2}{9} | = 9$

Step 1

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

$\frac{2 s - 2}{9} = \pm 9$

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.

$\frac{2 s - 2}{9} = 9$

Step 2.2

Multiply both sides by $9$ .

$\frac{2 s - 2}{9} \cdot 9 = 9 \cdot 9$

Step 2.3

Simplify.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Simplify $\frac{2 s - 2}{9} \cdot 9$ .

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Step 2.3.1.1.1

Factor $2$ out of $2 s - 2$ .

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Step 2.3.1.1.1.1

Factor $2$ out of $2 s$ .

$\frac{2 (s) - 2}{9} \cdot 9 = 9 \cdot 9$

Step 2.3.1.1.1.2

Factor $2$ out of $- 2$ .

$\frac{2 (s) + 2 (- 1)}{9} \cdot 9 = 9 \cdot 9$

Step 2.3.1.1.1.3

Factor $2$ out of $2 (s) + 2 (- 1)$ .

$\frac{2 (s - 1)}{9} \cdot 9 = 9 \cdot 9$

Step 2.3.1.1.2

Cancel the common factor of $9$ .

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Step 2.3.1.1.2.1

Cancel the common factor.

$\frac{2 (s - 1)}{9} \cdot 9 = 9 \cdot 9$

Step 2.3.1.1.2.2

Rewrite the expression.

$2 (s - 1) = 9 \cdot 9$

Step 2.3.1.1.3

Apply the distributive property.

$2 s + 2 \cdot - 1 = 9 \cdot 9$

Step 2.3.1.1.4

Multiply $2$ by $- 1$ .

$2 s - 2 = 9 \cdot 9$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Multiply $9$ by $9$ .

$2 s - 2 = 81$

Step 2.4

Solve for $s$ .

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Step 2.4.1

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

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Step 2.4.1.1

Add $2$ to both sides of the equation.

$2 s = 81 + 2$

Step 2.4.1.2

Add $81$ and $2$ .

$2 s = 83$

Step 2.4.2

Divide each term in $2 s = 83$ by $2$ and simplify.

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Step 2.4.2.1

Divide each term in $2 s = 83$ by $2$ .

$\frac{2 s}{2} = \frac{83}{2}$

Step 2.4.2.2

Simplify the left side.

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Step 2.4.2.2.1

Cancel the common factor of $2$ .

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Step 2.4.2.2.1.1

Cancel the common factor.

$\frac{2 s}{2} = \frac{83}{2}$

Step 2.4.2.2.1.2

Divide $s$ by $1$ .

$s = \frac{83}{2}$

Step 2.5

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

$\frac{2 s - 2}{9} = - 9$

Step 2.6

Multiply both sides by $9$ .

$\frac{2 s - 2}{9} \cdot 9 = - 9 \cdot 9$

Step 2.7

Simplify.

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Step 2.7.1

Simplify the left side.

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Step 2.7.1.1

Simplify $\frac{2 s - 2}{9} \cdot 9$ .

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Step 2.7.1.1.1

Factor $2$ out of $2 s - 2$ .

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Step 2.7.1.1.1.1

Factor $2$ out of $2 s$ .

$\frac{2 (s) - 2}{9} \cdot 9 = - 9 \cdot 9$

Step 2.7.1.1.1.2

Factor $2$ out of $- 2$ .

$\frac{2 (s) + 2 (- 1)}{9} \cdot 9 = - 9 \cdot 9$

Step 2.7.1.1.1.3

Factor $2$ out of $2 (s) + 2 (- 1)$ .

$\frac{2 (s - 1)}{9} \cdot 9 = - 9 \cdot 9$

Step 2.7.1.1.2

Cancel the common factor of $9$ .

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Step 2.7.1.1.2.1

Cancel the common factor.

$\frac{2 (s - 1)}{9} \cdot 9 = - 9 \cdot 9$

Step 2.7.1.1.2.2

Rewrite the expression.

$2 (s - 1) = - 9 \cdot 9$

Step 2.7.1.1.3

Apply the distributive property.

$2 s + 2 \cdot - 1 = - 9 \cdot 9$

Step 2.7.1.1.4

Multiply $2$ by $- 1$ .

$2 s - 2 = - 9 \cdot 9$

Step 2.7.2

Simplify the right side.

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Step 2.7.2.1

Multiply $- 9$ by $9$ .

$2 s - 2 = - 81$

Step 2.8

Solve for $s$ .

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Step 2.8.1

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

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Step 2.8.1.1

Add $2$ to both sides of the equation.

$2 s = - 81 + 2$

Step 2.8.1.2

Add $- 81$ and $2$ .

$2 s = - 79$

Step 2.8.2

Divide each term in $2 s = - 79$ by $2$ and simplify.

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Step 2.8.2.1

Divide each term in $2 s = - 79$ by $2$ .

$\frac{2 s}{2} = \frac{- 79}{2}$

Step 2.8.2.2

Simplify the left side.

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Step 2.8.2.2.1

Cancel the common factor of $2$ .

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Step 2.8.2.2.1.1

Cancel the common factor.

$\frac{2 s}{2} = \frac{- 79}{2}$

Step 2.8.2.2.1.2

Divide $s$ by $1$ .

$s = \frac{- 79}{2}$

Step 2.8.2.3

Simplify the right side.

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Step 2.8.2.3.1

Move the negative in front of the fraction.

$s = - \frac{79}{2}$

Step 2.9

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

$s = \frac{83}{2}, - \frac{79}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$s = \frac{83}{2}, - \frac{79}{2}$

Decimal Form:

$s = 41.5, - 39.5$

Mixed Number Form:

$s = 41 \frac{1}{2}, - 39 \frac{1}{2}$