Algebra Examples

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

Step 1

Simplify $\frac{3}{4} \cdot (- y + 1)$ .

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

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

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

Step 1.5

Multiply $\frac{3}{4}$ by $1$ .

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

Step 2

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

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Step 2.1

Add $\frac{3 y}{4}$ to both sides of the equation.

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

Step 2.2

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 2.3

Combine $2 y$ and $\frac{4}{4}$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $y$ out of $2 y \cdot 4 + 3 y$ .

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Step 2.5.1.1.1

Factor $y$ out of $2 y \cdot 4$ .

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

Step 2.5.1.1.2

Factor $y$ out of $3 y$ .

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

Step 2.5.1.1.3

Factor $y$ out of $y (2 \cdot 4) + y \cdot 3$ .

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

Step 2.5.1.2

Multiply $2$ by $4$ .

$- x + \frac{y (8 + 3)}{4} = \frac{3}{4}$

Step 2.5.1.3

Add $8$ and $3$ .

$- x + \frac{y \cdot 11}{4} = \frac{3}{4}$

Step 2.5.2

Move $11$ to the left of $y$ .

$- x + \frac{11 y}{4} = \frac{3}{4}$

Step 3

Add $x$ to both sides of the equation.

$\frac{11 y}{4} = \frac{3}{4} + x$

Step 4

Multiply both sides of the equation by $\frac{4}{11}$ .

$\frac{4}{11} \cdot \frac{11 y}{4} = \frac{4}{11} (\frac{3}{4} + x)$

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 $\frac{4}{11} \cdot \frac{11 y}{4}$ .

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Step 5.1.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{4}{11} \cdot \frac{11 y}{4} = \frac{4}{11} (\frac{3}{4} + x)$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{11} (11 y) = \frac{4}{11} (\frac{3}{4} + x)$

Step 5.1.1.2

Cancel the common factor of $11$ .

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Step 5.1.1.2.1

Factor $11$ out of $11 y$ .

$\frac{1}{11} (11 (y)) = \frac{4}{11} (\frac{3}{4} + x)$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{11} (11 y) = \frac{4}{11} (\frac{3}{4} + x)$

Step 5.1.1.2.3

Rewrite the expression.

$y = \frac{4}{11} (\frac{3}{4} + x)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{4}{11} (\frac{3}{4} + x)$ .

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Step 5.2.1.1

Apply the distributive property.

$y = \frac{4}{11} \cdot \frac{3}{4} + \frac{4}{11} x$

Step 5.2.1.2

Cancel the common factor of $4$ .

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Step 5.2.1.2.1

Cancel the common factor.

$y = \frac{4}{11} \cdot \frac{3}{4} + \frac{4}{11} x$

Step 5.2.1.2.2

Rewrite the expression.

$y = \frac{1}{11} \cdot 3 + \frac{4}{11} x$

Step 5.2.1.3

Combine $\frac{1}{11}$ and $3$ .

$y = \frac{3}{11} + \frac{4}{11} x$

Step 5.2.1.4

Combine $\frac{4}{11}$ and $x$ .

$y = \frac{3}{11} + \frac{4 x}{11}$

Step 6

Reorder $\frac{3}{11}$ and $\frac{4 x}{11}$ .

$y = \frac{4 x}{11} + \frac{3}{11}$