Basic Math Examples

$\frac{7 c - 4}{10} + \frac{2 c - 9}{5} + 2 = \frac{3 c - 4}{3} + 1$

Step 1

Simplify $\frac{7 c - 4}{10} + \frac{2 c - 9}{5} + 2$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Multiply $\frac{2 c - 9}{5}$ by $\frac{2}{2}$ .

$\frac{7 c - 4}{10} + \frac{2 c - 9}{5} \cdot \frac{2}{2} + 2 = \frac{3 c - 4}{3} + 1$

Step 1.1.2

Multiply $\frac{2 c - 9}{5}$ by $\frac{2}{2}$ .

$\frac{7 c - 4}{10} + \frac{(2 c - 9) \cdot 2}{5 \cdot 2} + 2 = \frac{3 c - 4}{3} + 1$

Step 1.1.3

Write $2$ as a fraction with denominator $1$ .

$\frac{7 c - 4}{10} + \frac{(2 c - 9) \cdot 2}{5 \cdot 2} + \frac{2}{1} = \frac{3 c - 4}{3} + 1$

Step 1.1.4

Multiply $\frac{2}{1}$ by $\frac{10}{10}$ .

$\frac{7 c - 4}{10} + \frac{(2 c - 9) \cdot 2}{5 \cdot 2} + \frac{2}{1} \cdot \frac{10}{10} = \frac{3 c - 4}{3} + 1$

Step 1.1.5

Multiply $\frac{2}{1}$ by $\frac{10}{10}$ .

$\frac{7 c - 4}{10} + \frac{(2 c - 9) \cdot 2}{5 \cdot 2} + \frac{2 \cdot 10}{10} = \frac{3 c - 4}{3} + 1$

Step 1.1.6

Reorder the factors of $5 \cdot 2$ .

$\frac{7 c - 4}{10} + \frac{(2 c - 9) \cdot 2}{2 \cdot 5} + \frac{2 \cdot 10}{10} = \frac{3 c - 4}{3} + 1$

Step 1.1.7

Multiply $2$ by $5$ .

$\frac{7 c - 4}{10} + \frac{(2 c - 9) \cdot 2}{10} + \frac{2 \cdot 10}{10} = \frac{3 c - 4}{3} + 1$

Step 1.2

Combine the numerators over the common denominator.

$\frac{7 c - 4 + (2 c - 9) \cdot 2 + 2 \cdot 10}{10} = \frac{3 c - 4}{3} + 1$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$\frac{7 c - 4 + 2 c \cdot 2 - 9 \cdot 2 + 2 \cdot 10}{10} = \frac{3 c - 4}{3} + 1$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{7 c - 4 + 4 c - 9 \cdot 2 + 2 \cdot 10}{10} = \frac{3 c - 4}{3} + 1$

Step 1.3.3

Multiply $- 9$ by $2$ .

$\frac{7 c - 4 + 4 c - 18 + 2 \cdot 10}{10} = \frac{3 c - 4}{3} + 1$

Step 1.3.4

Multiply $2$ by $10$ .

$\frac{7 c - 4 + 4 c - 18 + 20}{10} = \frac{3 c - 4}{3} + 1$

Step 1.4

Simplify by adding terms.

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Step 1.4.1

Add $7 c$ and $4 c$ .

$\frac{11 c - 4 - 18 + 20}{10} = \frac{3 c - 4}{3} + 1$

Step 1.4.2

Simplify by adding and subtracting.

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Step 1.4.2.1

Subtract $18$ from $- 4$ .

$\frac{11 c - 22 + 20}{10} = \frac{3 c - 4}{3} + 1$

Step 1.4.2.2

Add $- 22$ and $20$ .

$\frac{11 c - 2}{10} = \frac{3 c - 4}{3} + 1$

Step 2

Simplify $\frac{3 c - 4}{3} + 1$ .

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Step 2.1

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

$\frac{11 c - 2}{10} = \frac{3 c - 4}{3} + \frac{3}{3}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{11 c - 2}{10} = \frac{3 c - 4 + 3}{3}$

Step 2.3

Add $- 4$ and $3$ .

$\frac{11 c - 2}{10} = \frac{3 c - 1}{3}$

Step 3

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

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Step 3.1

Subtract $\frac{3 c - 1}{3}$ from both sides of the equation.

$\frac{11 c - 2}{10} - \frac{3 c - 1}{3} = 0$

Step 3.2

To write $\frac{11 c - 2}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{11 c - 2}{10} \cdot \frac{3}{3} - \frac{3 c - 1}{3} = 0$

Step 3.3

To write $- \frac{3 c - 1}{3}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{11 c - 2}{10} \cdot \frac{3}{3} - \frac{3 c - 1}{3} \cdot \frac{10}{10} = 0$

Step 3.4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{11 c - 2}{10}$ by $\frac{3}{3}$ .

$\frac{(11 c - 2) \cdot 3}{10 \cdot 3} - \frac{3 c - 1}{3} \cdot \frac{10}{10} = 0$

Step 3.4.2

Multiply $10$ by $3$ .

$\frac{(11 c - 2) \cdot 3}{30} - \frac{3 c - 1}{3} \cdot \frac{10}{10} = 0$

Step 3.4.3

Multiply $\frac{3 c - 1}{3}$ by $\frac{10}{10}$ .

$\frac{(11 c - 2) \cdot 3}{30} - \frac{(3 c - 1) \cdot 10}{3 \cdot 10} = 0$

Step 3.4.4

Multiply $3$ by $10$ .

$\frac{(11 c - 2) \cdot 3}{30} - \frac{(3 c - 1) \cdot 10}{30} = 0$

Step 3.5

Combine the numerators over the common denominator.

$\frac{(11 c - 2) \cdot 3 - (3 c - 1) \cdot 10}{30} = 0$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Apply the distributive property.

$\frac{11 c \cdot 3 - 2 \cdot 3 - (3 c - 1) \cdot 10}{30} = 0$

Step 3.6.2

Multiply $3$ by $11$ .

$\frac{33 c - 2 \cdot 3 - (3 c - 1) \cdot 10}{30} = 0$

Step 3.6.3

Multiply $- 2$ by $3$ .

$\frac{33 c - 6 - (3 c - 1) \cdot 10}{30} = 0$

Step 3.6.4

Apply the distributive property.

$\frac{33 c - 6 + (- (3 c) - - 1) \cdot 10}{30} = 0$

Step 3.6.5

Multiply $3$ by $- 1$ .

$\frac{33 c - 6 + (- 3 c - - 1) \cdot 10}{30} = 0$

Step 3.6.6

Multiply $- 1$ by $- 1$ .

$\frac{33 c - 6 + (- 3 c + 1) \cdot 10}{30} = 0$

Step 3.6.7

Apply the distributive property.

$\frac{33 c - 6 - 3 c \cdot 10 + 1 \cdot 10}{30} = 0$

Step 3.6.8

Multiply $10$ by $- 3$ .

$\frac{33 c - 6 - 30 c + 1 \cdot 10}{30} = 0$

Step 3.6.9

Multiply $10$ by $1$ .

$\frac{33 c - 6 - 30 c + 10}{30} = 0$

Step 3.6.10

Subtract $30 c$ from $33 c$ .

$\frac{3 c - 6 + 10}{30} = 0$

Step 3.6.11

Add $- 6$ and $10$ .

$\frac{3 c + 4}{30} = 0$

Step 4

Set the numerator equal to zero.

$3 c + 4 = 0$

Step 5

Solve the equation for $c$ .

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Step 5.1

Subtract $4$ from both sides of the equation.

$3 c = - 4$

Step 5.2

Divide each term in $3 c = - 4$ by $3$ and simplify.

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Step 5.2.1

Divide each term in $3 c = - 4$ by $3$ .

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

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $3$ .

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Step 5.2.2.1.1

Cancel the common factor.

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

Step 5.2.2.1.2

Divide $c$ by $1$ .

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

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$c = - 1.\overline{3}$

Mixed Number Form:

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