Pre-Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Move $3$ to the left of $y$ .

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

Step 2

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

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Step 2.1

Subtract $\frac{1}{4}$ from both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Multiply $2$ by $2$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Subtract $1$ from $2$ .

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

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 3 y = 1$

Step 4

Divide each term in $- 3 y = 1$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 y = 1$ by $- 3$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $y$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = - 0.\overline{3}$