Finite Math Examples

$- 8 = - \frac{3}{2} c + 6$

Step 1

Rewrite the equation as $- \frac{3}{2} c + 6 = - 8$ .

$- \frac{3}{2} c + 6 = - 8$

Step 2

Simplify each term.

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Step 2.1

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

$- \frac{c \cdot 3}{2} + 6 = - 8$

Step 2.2

Move $3$ to the left of $c$ .

$- \frac{3 c}{2} + 6 = - 8$

Step 3

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

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Step 3.1

Subtract $6$ from both sides of the equation.

$- \frac{3 c}{2} = - 8 - 6$

Step 3.2

Subtract $6$ from $- 8$ .

$- \frac{3 c}{2} = - 14$

Step 4

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

$- \frac{2}{3} (- \frac{3 c}{2}) = - \frac{2}{3} \cdot - 14$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{2}{3} (- \frac{3 c}{2})$ .

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- \frac{3 c}{2}) = - \frac{2}{3} \cdot - 14$

Step 5.1.1.1.2

Move the leading negative in $- \frac{3 c}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 c}{2} = - \frac{2}{3} \cdot - 14$

Step 5.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 c}{2} = - \frac{2}{3} \cdot - 14$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 c}{2} = - \frac{2}{3} \cdot - 14$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 c) = - \frac{2}{3} \cdot - 14$

Step 5.1.1.2

Cancel the common factor of $3$ .

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Step 5.1.1.2.1

Factor $3$ out of $- 3 c$ .

$\frac{- 1}{3} (3 (- c)) = - \frac{2}{3} \cdot - 14$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- c)) = - \frac{2}{3} \cdot - 14$

Step 5.1.1.2.3

Rewrite the expression.

$- - c = - \frac{2}{3} \cdot - 14$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 c = - \frac{2}{3} \cdot - 14$

Step 5.1.1.3.2

Multiply $c$ by $1$ .

$c = - \frac{2}{3} \cdot - 14$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- \frac{2}{3} \cdot - 14$ .

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Step 5.2.1.1

Multiply $- 14$ by $- 1$ .

$c = 14 (\frac{2}{3})$

Step 5.2.1.2

Combine $14$ and $\frac{2}{3}$ .

$c = \frac{14 \cdot 2}{3}$

Step 5.2.1.3

Multiply $14$ by $2$ .

$c = \frac{28}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$c = \frac{28}{3}$

Decimal Form:

$c = 9.\overline{3}$

Mixed Number Form:

$c = 9 \frac{1}{3}$