Algebra Examples

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

Step 1

Combine $\frac{3}{4}$ and $y$ .

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

Step 2

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

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Step 2.1

Subtract $y$ from both sides of the equation.

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

Step 2.2

To write $- y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 2.3

Combine $- y$ and $\frac{4}{4}$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Combine the numerators over the common denominator.

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

Step 2.6

Multiply $4$ by $- 1$ .

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

Step 2.7

Subtract $4 y$ from $3 y$ .

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

Step 2.8

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

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

Step 2.9

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

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

Step 2.10

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

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

Step 2.11

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

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

Step 2.12

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- 4 (- \frac{y - 1}{4})$ .

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Step 4.1.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{y - 1}{4}$ into the numerator.

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

Step 4.1.1.1.2

Factor $4$ out of $- 4$ .

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

Step 4.1.1.1.3

Cancel the common factor.

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

Step 4.1.1.1.4

Rewrite the expression.

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

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

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

Step 4.1.1.2.2

Multiply $y - 1$ by $1$ .

$y - 1 = - 4 \cdot 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 4$ by $1$ .

$y - 1 = - 4$

Step 5

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

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Step 5.1

Add $1$ to both sides of the equation.

$y = - 4 + 1$

Step 5.2

Add $- 4$ and $1$ .

$y = - 3$