Basic Math Examples

$\frac{1}{7} \cdot (c - 3) = \frac{2}{7} c + \frac{- 22}{7}$

Step 1

Simplify $\frac{1}{7} \cdot (c - 3)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{7} \cdot (c - 3) = \frac{2}{7} c + \frac{- 22}{7}$

Step 1.2

Simplify by adding zeros.

$\frac{1}{7} \cdot (c - 3) = \frac{2}{7} c + \frac{- 22}{7}$

Step 1.3

Apply the distributive property.

$\frac{1}{7} c + \frac{1}{7} \cdot - 3 = \frac{2}{7} c + \frac{- 22}{7}$

Step 1.4

Combine $\frac{1}{7}$ and $c$ .

$\frac{c}{7} + \frac{1}{7} \cdot - 3 = \frac{2}{7} c + \frac{- 22}{7}$

Step 1.5

Combine $\frac{1}{7}$ and $- 3$ .

$\frac{c}{7} + \frac{- 3}{7} = \frac{2}{7} c + \frac{- 22}{7}$

Step 1.6

Move the negative in front of the fraction.

$\frac{c}{7} - \frac{3}{7} = \frac{2}{7} c + \frac{- 22}{7}$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{2}{7}$ and $c$ .

$\frac{c}{7} - \frac{3}{7} = \frac{2 c}{7} + \frac{- 22}{7}$

Step 2.2

Move the negative in front of the fraction.

$\frac{c}{7} - \frac{3}{7} = \frac{2 c}{7} - \frac{22}{7}$

Step 3

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

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Step 3.1

Subtract $\frac{2 c}{7}$ from both sides of the equation.

$\frac{c}{7} - \frac{3}{7} - \frac{2 c}{7} = - \frac{22}{7}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{c - 3 - 2 c}{7} = - \frac{22}{7}$

Step 3.3

Subtract $2 c$ from $c$ .

$\frac{- c - 3}{7} = - \frac{22}{7}$

Step 3.4

Factor $- 1$ out of $- c$ .

$\frac{- (c) - 3}{7} = - \frac{22}{7}$

Step 3.5

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- (c) - 1 (3)}{7} = - \frac{22}{7}$

Step 3.6

Factor $- 1$ out of $- (c) - 1 (3)$ .

$\frac{- (c + 3)}{7} = - \frac{22}{7}$

Step 3.7

Rewrite $- (c + 3)$ as $- 1 (c + 3)$ .

$\frac{- 1 (c + 3)}{7} = - \frac{22}{7}$

Step 3.8

Move the negative in front of the fraction.

$- \frac{c + 3}{7} = - \frac{22}{7}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- (c + 3) = - 22$

Step 5

Simplify $- (c + 3)$ .

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Step 5.1

Apply the distributive property.

$- c - 1 \cdot 3 = - 22$

Step 5.2

Multiply $- 1$ by $3$ .

$- c - 3 = - 22$

Step 6

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

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Step 6.1

Add $3$ to both sides of the equation.

$- c = - 22 + 3$

Step 6.2

Add $- 22$ and $3$ .

$- c = - 19$

Step 7

Divide each term in $- c = - 19$ by $- 1$ and simplify.

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Step 7.1

Divide each term in $- c = - 19$ by $- 1$ .

$\frac{- c}{- 1} = \frac{- 19}{- 1}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Dividing two negative values results in a positive value.

$\frac{c}{1} = \frac{- 19}{- 1}$

Step 7.2.2

Divide $c$ by $1$ .

$c = \frac{- 19}{- 1}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Divide $- 19$ by $- 1$ .

$c = 19$