Algebra Examples

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

Step 1

Simplify $\frac{y}{4} - \frac{y - 1}{2}$ .

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Step 1.1

To write $- \frac{y - 1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{y - 1}{2}$ by $\frac{2}{2}$ .

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

Step 1.2.2

Multiply $2$ by $2$ .

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Simplify the numerator.

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Step 1.4.1

Apply the distributive property.

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

Step 1.4.2

Multiply $- 1$ by $- 1$ .

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

Step 1.4.3

Apply the distributive property.

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

Step 1.4.4

Multiply $2$ by $- 1$ .

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

Step 1.4.5

Multiply $2$ by $1$ .

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

Step 1.4.6

Subtract $2 y$ from $y$ .

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

Step 1.5

Simplify with factoring out.

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Step 1.5.1

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

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

Step 1.5.2

Rewrite $2$ as $- 1 (- 2)$ .

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

Step 1.5.3

Factor $- 1$ out of $- (y) - 1 (- 2)$ .

$\frac{- (y - 2)}{4} = 3$

Step 1.5.4

Simplify the expression.

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Step 1.5.4.1

Rewrite $- (y - 2)$ as $- 1 (y - 2)$ .

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

Step 1.5.4.2

Move the negative in front of the fraction.

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

Step 2

Multiply both sides of the equation by $- 4$ .

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

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 $- 4 (- \frac{y - 2}{4})$ .

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Step 3.1.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{y - 2}{4}$ into the numerator.

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

Step 3.1.1.1.2

Factor $4$ out of $- 4$ .

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

Step 3.1.1.1.3

Cancel the common factor.

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

Step 3.1.1.1.4

Rewrite the expression.

$- - (y - 2) = - 4 \cdot 3$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (y - 2) = - 4 \cdot 3$

Step 3.1.1.2.2

Multiply $y - 2$ by $1$ .

$y - 2 = - 4 \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 4$ by $3$ .

$y - 2 = - 12$

Step 4

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

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Step 4.1

Add $2$ to both sides of the equation.

$y = - 12 + 2$

Step 4.2

Add $- 12$ and $2$ .

$y = - 10$