Basic Math Examples

$4 y + \frac{7}{4} = 5 y - \frac{7}{4}$

Step 1

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

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Step 1.1

Subtract $5 y$ from both sides of the equation.

$4 y + \frac{7}{4} - 5 y = - \frac{7}{4}$

Step 1.2

Subtract $5 y$ from $4 y$ .

$- y + \frac{7}{4} = - \frac{7}{4}$

Step 2

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

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Step 2.1

Subtract $\frac{7}{4}$ from both sides of the equation.

$- y = - \frac{7}{4} - \frac{7}{4}$

Step 2.2

Combine the numerators over the common denominator.

$- y = \frac{- 7 - 7}{4}$

Step 2.3

Subtract $7$ from $- 7$ .

$- y = \frac{- 14}{4}$

Step 2.4

Cancel the common factor of $- 14$ and $4$ .

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Step 2.4.1

Factor $2$ out of $- 14$ .

$- y = \frac{2 (- 7)}{4}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $4$ .

$- y = \frac{2 \cdot - 7}{2 \cdot 2}$

Step 2.4.2.2

Cancel the common factor.

$- y = \frac{2 \cdot - 7}{2 \cdot 2}$

Step 2.4.2.3

Rewrite the expression.

$- y = \frac{- 7}{2}$

Step 2.5

Move the negative in front of the fraction.

$- y = - \frac{7}{2}$

Step 3

Divide each term in $- y = - \frac{7}{2}$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- y = - \frac{7}{2}$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- \frac{7}{2}}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- \frac{7}{2}}{- 1}$

Step 3.2.2

Divide $y$ by $1$ .

$y = \frac{- \frac{7}{2}}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

$y = \frac{\frac{7}{2}}{1}$

Step 3.3.2

Divide $\frac{7}{2}$ by $1$ .

$y = \frac{7}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{7}{2}$

Decimal Form:

$y = 3.5$

Mixed Number Form:

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