Algebra Examples

$\frac{5}{9} c - \frac{3}{4} = \frac{7}{9} c$

Step 1

Combine $\frac{5}{9}$ and $c$ .

$\frac{5 c}{9} - \frac{3}{4} = \frac{7}{9} c$

Step 2

Combine $\frac{7}{9}$ and $c$ .

$\frac{5 c}{9} - \frac{3}{4} = \frac{7 c}{9}$

Step 3

Move all terms containing $c$ to the left side of the equation.

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Step 3.1

Subtract $\frac{7 c}{9}$ from both sides of the equation.

$\frac{5 c}{9} - \frac{3}{4} - \frac{7 c}{9} = 0$

Step 3.2

Combine the numerators over the common denominator.

$\frac{5 c - 7 c}{9} + \frac{- 3}{4} = 0$

Step 3.3

Subtract $7 c$ from $5 c$ .

$\frac{- 2 c}{9} + \frac{- 3}{4} = 0$

Step 3.4

Simplify each term.

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Step 3.4.1

Move the negative in front of the fraction.

$- \frac{2 c}{9} + \frac{- 3}{4} = 0$

Step 3.4.2

Move the negative in front of the fraction.

$- \frac{2 c}{9} - \frac{3}{4} = 0$

Step 4

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

$- \frac{2 c}{9} = \frac{3}{4}$

Step 5

Multiply both sides of the equation by $- \frac{9}{2}$ .

$- \frac{9}{2} (- \frac{2 c}{9}) = - \frac{9}{2} \cdot \frac{3}{4}$

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 $- \frac{9}{2} (- \frac{2 c}{9})$ .

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Step 6.1.1.1

Cancel the common factor of $9$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$\frac{- 9}{2} (- \frac{2 c}{9}) = - \frac{9}{2} \cdot \frac{3}{4}$

Step 6.1.1.1.2

Move the leading negative in $- \frac{2 c}{9}$ into the numerator.

$\frac{- 9}{2} \cdot \frac{- 2 c}{9} = - \frac{9}{2} \cdot \frac{3}{4}$

Step 6.1.1.1.3

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{2} \cdot \frac{- 2 c}{9} = - \frac{9}{2} \cdot \frac{3}{4}$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{9 \cdot - 1}{2} \cdot \frac{- 2 c}{9} = - \frac{9}{2} \cdot \frac{3}{4}$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} (- 2 c) = - \frac{9}{2} \cdot \frac{3}{4}$

Step 6.1.1.2

Cancel the common factor of $2$ .

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Step 6.1.1.2.1

Factor $2$ out of $- 2 c$ .

$\frac{- 1}{2} (2 (- c)) = - \frac{9}{2} \cdot \frac{3}{4}$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} (2 (- c)) = - \frac{9}{2} \cdot \frac{3}{4}$

Step 6.1.1.2.3

Rewrite the expression.

$- - c = - \frac{9}{2} \cdot \frac{3}{4}$

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 c = - \frac{9}{2} \cdot \frac{3}{4}$

Step 6.1.1.3.2

Multiply $c$ by $1$ .

$c = - \frac{9}{2} \cdot \frac{3}{4}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- \frac{9}{2} \cdot \frac{3}{4}$ .

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Step 6.2.1.1

Multiply $\frac{3}{4}$ by $\frac{9}{2}$ .

$c = - \frac{3 \cdot 9}{4 \cdot 2}$

Step 6.2.1.2

Multiply $3$ by $9$ .

$c = - \frac{27}{4 \cdot 2}$

Step 6.2.1.3

Multiply $4$ by $2$ .

$c = - \frac{27}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$c = - \frac{27}{8}$

Decimal Form:

$c = - 3.375$

Mixed Number Form:

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