Basic Math Examples

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

Step 1

Simplify $\frac{3}{2} \cdot (c - 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{3}{2} \cdot (c - 1) = \frac{1}{2} \cdot (4 c) + 1$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

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

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

Step 1.5

Multiply $\frac{3}{2} \cdot - 1$ .

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Step 1.5.1

Combine $\frac{3}{2}$ and $- 1$ .

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

Step 1.5.2

Multiply $3$ by $- 1$ .

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

Step 1.6

Move the negative in front of the fraction.

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

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $4 c$ .

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

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

Step 3

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

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Step 3.1

Subtract $2 c$ from both sides of the equation.

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Combine the numerators over the common denominator.

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

Step 3.6

Multiply $2$ by $- 2$ .

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

Step 3.7

Subtract $4 c$ from $3 c$ .

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

Step 3.8

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

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

Step 3.9

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

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

Step 3.10

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

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

Step 3.11

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

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

Step 3.12

Move the negative in front of the fraction.

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

Step 4

Multiply both sides of the equation by $- 2$ .

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

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

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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 $- \frac{c + 3}{2}$ into the numerator.

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

Step 5.1.1.1.2

Factor $2$ out of $- 2$ .

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

Step 5.1.1.1.3

Cancel the common factor.

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

Step 5.1.1.1.4

Rewrite the expression.

$- - (c + 3) = - 2 \cdot 1$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (c + 3) = - 2 \cdot 1$

Step 5.1.1.2.2

Multiply $c + 3$ by $1$ .

$c + 3 = - 2 \cdot 1$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 2$ by $1$ .

$c + 3 = - 2$

Step 6

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

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Step 6.1

Subtract $3$ from both sides of the equation.

$c = - 2 - 3$

Step 6.2

Subtract $3$ from $- 2$ .

$c = - 5$