Basic Math Examples

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

Step 1

Simplify $2 (1 - y) - \frac{1}{2} \cdot (y + 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Multiply $2$ by $1$ .

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

Step 1.1.3

Multiply $- 1$ by $2$ .

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

Step 1.1.4

Apply the distributive property.

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

Step 1.1.5

Combine $y$ and $\frac{1}{2}$ .

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

Step 1.1.6

Multiply $- 1$ by $1$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $2$ by $2$ .

$- 2 y - \frac{y}{2} + \frac{4 - 1}{2} = 3$

Step 1.5.2

Subtract $1$ from $4$ .

$- 2 y - \frac{y}{2} + \frac{3}{2} = 3$

Step 1.6

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

$- 2 y \cdot \frac{2}{2} - \frac{y}{2} + \frac{3}{2} = 3$

Step 1.7

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

$\frac{- 2 y \cdot 2}{2} - \frac{y}{2} + \frac{3}{2} = 3$

Step 1.8

Combine the numerators over the common denominator.

$\frac{- 2 y \cdot 2 - y}{2} + \frac{3}{2} = 3$

Step 1.9

Combine the numerators over the common denominator.

$\frac{- 2 y \cdot 2 - y + 3}{2} = 3$

Step 1.10

Multiply $2$ by $- 2$ .

$\frac{- 4 y - y + 3}{2} = 3$

Step 1.11

Subtract $y$ from $- 4 y$ .

$\frac{- 5 y + 3}{2} = 3$

Step 1.12

Factor $- 1$ out of $- 5 y$ .

$\frac{- (5 y) + 3}{2} = 3$

Step 1.13

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

$\frac{- (5 y) - 1 (- 3)}{2} = 3$

Step 1.14

Factor $- 1$ out of $- (5 y) - 1 (- 3)$ .

$\frac{- (5 y - 3)}{2} = 3$

Step 1.15

Simplify the expression.

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Step 1.15.1

Rewrite $- (5 y - 3)$ as $- 1 (5 y - 3)$ .

$\frac{- 1 (5 y - 3)}{2} = 3$

Step 1.15.2

Move the negative in front of the fraction.

$- \frac{5 y - 3}{2} = 3$

Step 2

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

$- 2 (- \frac{5 y - 3}{2}) = - 2 \cdot 3$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- 2 (- \frac{5 y - 3}{2})$ .

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Step 3.1.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{5 y - 3}{2}$ into the numerator.

$- 2 \frac{- (5 y - 3)}{2} = - 2 \cdot 3$

Step 3.1.1.1.2

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- (5 y - 3)}{2} = - 2 \cdot 3$

Step 3.1.1.1.3

Cancel the common factor.

$2 \cdot - 1 \frac{- (5 y - 3)}{2} = - 2 \cdot 3$

Step 3.1.1.1.4

Rewrite the expression.

$- - (5 y - 3) = - 2 \cdot 3$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (5 y - 3) = - 2 \cdot 3$

Step 3.1.1.2.2

Multiply $5 y - 3$ by $1$ .

$5 y - 3 = - 2 \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 2$ by $3$ .

$5 y - 3 = - 6$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$5 y = - 6 + 3$

Step 4.2

Add $- 6$ and $3$ .

$5 y = - 3$

Step 5

Divide each term in $5 y = - 3$ by $5$ and simplify.

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Step 5.1

Divide each term in $5 y = - 3$ by $5$ .

$\frac{5 y}{5} = \frac{- 3}{5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 3}{5}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 3}{5}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$y = - \frac{3}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{3}{5}$

Decimal Form:

$y = - 0.6$