Finite Math Examples

$\frac{g \cdot 3}{2} = \frac{3^{2}}{2} + 1$

Step 1

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{g \cdot 3}{2} = \frac{2}{3} (\frac{3^{2}}{2} + 1)$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{2}{3} \cdot \frac{g \cdot 3}{2}$ .

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Step 2.1.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{g \cdot 3}{2} = \frac{2}{3} (\frac{3^{2}}{2} + 1)$

Step 2.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (g \cdot 3) = \frac{2}{3} (\frac{3^{2}}{2} + 1)$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Factor $3$ out of $g \cdot 3$ .

$\frac{1}{3} (3 \cdot g) = \frac{2}{3} (\frac{3^{2}}{2} + 1)$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 \cdot g) = \frac{2}{3} (\frac{3^{2}}{2} + 1)$

Step 2.1.1.2.3

Rewrite the expression.

$g = \frac{2}{3} (\frac{3^{2}}{2} + 1)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{2}{3} (\frac{3^{2}}{2} + 1)$ .

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Step 2.2.1.1

Simplify the expression.

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Step 2.2.1.1.1

Raise $3$ to the power of $2$ .

$g = \frac{2}{3} (\frac{9}{2} + 1)$

Step 2.2.1.1.2

Write $1$ as a fraction with a common denominator.

$g = \frac{2}{3} (\frac{9}{2} + \frac{2}{2})$

Step 2.2.1.1.3

Combine the numerators over the common denominator.

$g = \frac{2}{3} \cdot \frac{9 + 2}{2}$

Step 2.2.1.1.4

Add $9$ and $2$ .

$g = \frac{2}{3} \cdot \frac{11}{2}$

Step 2.2.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.2.1

Cancel the common factor.

$g = \frac{2}{3} \cdot \frac{11}{2}$

Step 2.2.1.2.2

Rewrite the expression.

$g = \frac{1}{3} \cdot 11$

Step 2.2.1.3

Combine $\frac{1}{3}$ and $11$ .

$g = \frac{11}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$g = \frac{11}{3}$

Decimal Form:

$g = 3.\overline{6}$

Mixed Number Form:

$g = 3 \frac{2}{3}$