Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

Subtract $\frac{3 y}{4}$ from both sides of the equation.

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

Step 3.2

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

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

Step 3.3

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

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Step 3.3.1

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

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

Step 3.3.2

Multiply $2$ by $2$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Subtract $3 y$ from $y \cdot 2$ .

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Step 3.5.1

Reorder $y$ and $2$ .

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

Step 3.5.2

Subtract $3 y$ from $2 \cdot y$ .

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

Step 3.6

Move the negative in front of the fraction.

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

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.

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

Step 4.2

Add $1$ and $2$ .

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

Step 5

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

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

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

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

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Step 6.1.1.1

Cancel the common factor of $4$ .

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Step 6.1.1.1.1

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

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

Step 6.1.1.1.2

Factor $4$ out of $- 4$ .

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

Step 6.1.1.1.3

Cancel the common factor.

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

Step 6.1.1.1.4

Rewrite the expression.

$- - y = - 4 \cdot 3$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 4 \cdot 3$

Step 6.1.1.2.2

Multiply $y$ by $1$ .

$y = - 4 \cdot 3$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 4$ by $3$ .

$y = - 12$