Finite Math Examples

$a \cdot 1 = - \frac{3}{4} + \frac{3}{2} n$

Step 1

Rewrite the equation as $- \frac{3}{4} + \frac{3}{2} n = a \cdot 1$ .

$- \frac{3}{4} + \frac{3}{2} n = a \cdot 1$

Step 2

Combine $\frac{3}{2}$ and $n$ .

$- \frac{3}{4} + \frac{3 n}{2} = a \cdot 1$

Step 3

Multiply $a$ by $1$ .

$- \frac{3}{4} + \frac{3 n}{2} = a$

Step 4

Add $\frac{3}{4}$ to both sides of the equation.

$\frac{3 n}{2} = a + \frac{3}{4}$

Step 5

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

$\frac{2}{3} \cdot \frac{3 n}{2} = \frac{2}{3} (a + \frac{3}{4})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

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

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Step 6.1.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 n}{2} = \frac{2}{3} (a + \frac{3}{4})$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 n) = \frac{2}{3} (a + \frac{3}{4})$

Step 6.1.1.2

Cancel the common factor of $3$ .

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Step 6.1.1.2.1

Factor $3$ out of $3 n$ .

$\frac{1}{3} (3 (n)) = \frac{2}{3} (a + \frac{3}{4})$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 n) = \frac{2}{3} (a + \frac{3}{4})$

Step 6.1.1.2.3

Rewrite the expression.

$n = \frac{2}{3} (a + \frac{3}{4})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{2}{3} (a + \frac{3}{4})$ .

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Step 6.2.1.1

Apply the distributive property.

$n = \frac{2}{3} a + \frac{2}{3} \cdot \frac{3}{4}$

Step 6.2.1.2

Combine $\frac{2}{3}$ and $a$ .

$n = \frac{2 a}{3} + \frac{2}{3} \cdot \frac{3}{4}$

Step 6.2.1.3

Cancel the common factor of $2$ .

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Step 6.2.1.3.1

Factor $2$ out of $4$ .

$n = \frac{2 a}{3} + \frac{2}{3} \cdot \frac{3}{2 (2)}$

Step 6.2.1.3.2

Cancel the common factor.

$n = \frac{2 a}{3} + \frac{2}{3} \cdot \frac{3}{2 \cdot 2}$

Step 6.2.1.3.3

Rewrite the expression.

$n = \frac{2 a}{3} + \frac{1}{3} \cdot \frac{3}{2}$

Step 6.2.1.4

Cancel the common factor of $3$ .

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Step 6.2.1.4.1

Cancel the common factor.

$n = \frac{2 a}{3} + \frac{1}{3} \cdot \frac{3}{2}$

Step 6.2.1.4.2

Rewrite the expression.

$n = \frac{2 a}{3} + \frac{1}{2}$