Finite Math Examples

$\frac{x + 9}{2} - \frac{x - 9}{9} = 1$

Step 1

Simplify $\frac{x + 9}{2} - \frac{x - 9}{9}$ .

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Step 1.1

To write $\frac{x + 9}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{x + 9}{2} \cdot \frac{9}{9} - \frac{x - 9}{9} = 1$

Step 1.2

To write $- \frac{x - 9}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x + 9}{2} \cdot \frac{9}{9} - \frac{x - 9}{9} \cdot \frac{2}{2} = 1$

Step 1.3

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x + 9}{2}$ by $\frac{9}{9}$ .

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

Step 1.3.2

Multiply $2$ by $9$ .

$\frac{(x + 9) \cdot 9}{18} - \frac{x - 9}{9} \cdot \frac{2}{2} = 1$

Step 1.3.3

Multiply $\frac{x - 9}{9}$ by $\frac{2}{2}$ .

$\frac{(x + 9) \cdot 9}{18} - \frac{(x - 9) \cdot 2}{9 \cdot 2} = 1$

Step 1.3.4

Multiply $9$ by $2$ .

$\frac{(x + 9) \cdot 9}{18} - \frac{(x - 9) \cdot 2}{18} = 1$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(x + 9) \cdot 9 - (x - 9) \cdot 2}{18} = 1$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{x \cdot 9 + 9 \cdot 9 - (x - 9) \cdot 2}{18} = 1$

Step 1.5.2

Move $9$ to the left of $x$ .

$\frac{9 \cdot x + 9 \cdot 9 - (x - 9) \cdot 2}{18} = 1$

Step 1.5.3

Multiply $9$ by $9$ .

$\frac{9 \cdot x + 81 - (x - 9) \cdot 2}{18} = 1$

Step 1.5.4

Apply the distributive property.

$\frac{9 x + 81 + (- x - - 9) \cdot 2}{18} = 1$

Step 1.5.5

Multiply $- 1$ by $- 9$ .

$\frac{9 x + 81 + (- x + 9) \cdot 2}{18} = 1$

Step 1.5.6

Apply the distributive property.

$\frac{9 x + 81 - x \cdot 2 + 9 \cdot 2}{18} = 1$

Step 1.5.7

Multiply $2$ by $- 1$ .

$\frac{9 x + 81 - 2 x + 9 \cdot 2}{18} = 1$

Step 1.5.8

Multiply $9$ by $2$ .

$\frac{9 x + 81 - 2 x + 18}{18} = 1$

Step 1.5.9

Subtract $2 x$ from $9 x$ .

$\frac{7 x + 81 + 18}{18} = 1$

Step 1.5.10

Add $81$ and $18$ .

$\frac{7 x + 99}{18} = 1$

Step 2

Multiply both sides by $18$ .

$\frac{7 x + 99}{18} \cdot 18 = 1 \cdot 18$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $18$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{7 x + 99}{18} \cdot 18 = 1 \cdot 18$

Step 3.1.1.2

Rewrite the expression.

$7 x + 99 = 1 \cdot 18$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $18$ by $1$ .

$7 x + 99 = 18$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $99$ from both sides of the equation.

$7 x = 18 - 99$

Step 4.1.2

Subtract $99$ from $18$ .

$7 x = - 81$

Step 4.2

Divide each term in $7 x = - 81$ by $7$ and simplify.

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Step 4.2.1

Divide each term in $7 x = - 81$ by $7$ .

$\frac{7 x}{7} = \frac{- 81}{7}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $7$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 81}{7}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 81}{7}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$x = - \frac{81}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{81}{7}$

Decimal Form:

$x = - 11.57142857 \dots$

Mixed Number Form:

$x = - 11 \frac{4}{7}$