Algebra Examples

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

Step 1

Rewrite the equation as $- \frac{1}{2} - y = \frac{3}{4}$ .

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

Step 2

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

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Step 2.1

Add $\frac{1}{2}$ to both sides of the equation.

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

Step 2.2

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

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

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 $\frac{2}{2}$ .

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

Step 2.3.2

Multiply $2$ by $2$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Add $3$ and $2$ .

$- y = \frac{5}{4}$

Step 3

Divide each term in $- y = \frac{5}{4}$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- y = \frac{5}{4}$ by $- 1$ .

$\frac{- y}{- 1} = \frac{\frac{5}{4}}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{\frac{5}{4}}{- 1}$

Step 3.2.2

Divide $y$ by $1$ .

$y = \frac{\frac{5}{4}}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative one from the denominator of $\frac{\frac{5}{4}}{- 1}$ .

$y = - 1 \cdot \frac{5}{4}$

Step 3.3.2

Rewrite $- 1 \cdot \frac{5}{4}$ as $- \frac{5}{4}$ .

$y = - \frac{5}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{5}{4}$

Decimal Form:

$y = - 1.25$

Mixed Number Form:

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