Finite Math Examples

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

Step 1

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

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Step 1.1

Subtract $\frac{9}{2}$ from both sides of the equation.

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

Step 1.2

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

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

Step 1.3

Combine $9$ and $\frac{2}{2}$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $9$ by $2$ .

$- y = \frac{18 - 9}{2}$

Step 1.5.2

Subtract $9$ from $18$ .

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

Step 2

Divide each term in $- y = \frac{9}{2}$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- y = \frac{9}{2}$ by $- 1$ .

$\frac{- y}{- 1} = \frac{\frac{9}{2}}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{\frac{9}{2}}{- 1}$

Step 2.2.2

Divide $y$ by $1$ .

$y = \frac{\frac{9}{2}}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative one from the denominator of $\frac{\frac{9}{2}}{- 1}$ .

$y = - 1 \cdot \frac{9}{2}$

Step 2.3.2

Rewrite $- 1 \cdot \frac{9}{2}$ as $- \frac{9}{2}$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = - 4.5$

Mixed Number Form:

$y = - 4 \frac{1}{2}$