Finite Math Examples

$1 - \frac{5}{4} y = \frac{9}{4} - \frac{3}{8} y$

Step 1

Simplify each term.

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Step 1.1

Combine $y$ and $\frac{5}{4}$ .

$1 - \frac{y \cdot 5}{4} = \frac{9}{4} - \frac{3}{8} y$

Step 1.2

Move $5$ to the left of $y$ .

$1 - \frac{5 y}{4} = \frac{9}{4} - \frac{3}{8} y$

Step 2

Simplify each term.

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Step 2.1

Combine $y$ and $\frac{3}{8}$ .

$1 - \frac{5 y}{4} = \frac{9}{4} - \frac{y \cdot 3}{8}$

Step 2.2

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

$1 - \frac{5 y}{4} = \frac{9}{4} - \frac{3 y}{8}$

Step 3

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

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Step 3.1

Add $\frac{3 y}{8}$ to both sides of the equation.

$1 - \frac{5 y}{4} + \frac{3 y}{8} = \frac{9}{4}$

Step 3.2

To write $- \frac{5 y}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$1 - \frac{5 y}{4} \cdot \frac{2}{2} + \frac{3 y}{8} = \frac{9}{4}$

Step 3.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{5 y}{4}$ by $\frac{2}{2}$ .

$1 - \frac{5 y \cdot 2}{4 \cdot 2} + \frac{3 y}{8} = \frac{9}{4}$

Step 3.3.2

Multiply $4$ by $2$ .

$1 - \frac{5 y \cdot 2}{8} + \frac{3 y}{8} = \frac{9}{4}$

Step 3.4

Combine the numerators over the common denominator.

$1 + \frac{- 5 y \cdot 2 + 3 y}{8} = \frac{9}{4}$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $y$ out of $- 5 y \cdot 2 + 3 y$ .

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Step 3.5.1.1.1

Factor $y$ out of $- 5 y \cdot 2$ .

$1 + \frac{y (- 5 \cdot 2) + 3 y}{8} = \frac{9}{4}$

Step 3.5.1.1.2

Factor $y$ out of $3 y$ .

$1 + \frac{y (- 5 \cdot 2) + y \cdot 3}{8} = \frac{9}{4}$

Step 3.5.1.1.3

Factor $y$ out of $y (- 5 \cdot 2) + y \cdot 3$ .

$1 + \frac{y (- 5 \cdot 2 + 3)}{8} = \frac{9}{4}$

Step 3.5.1.2

Multiply $- 5$ by $2$ .

$1 + \frac{y (- 10 + 3)}{8} = \frac{9}{4}$

Step 3.5.1.3

Add $- 10$ and $3$ .

$1 + \frac{y \cdot - 7}{8} = \frac{9}{4}$

Step 3.5.2

Move $- 7$ to the left of $y$ .

$1 + \frac{- 7 \cdot y}{8} = \frac{9}{4}$

Step 3.5.3

Move the negative in front of the fraction.

$1 - \frac{7 y}{8} = \frac{9}{4}$

Step 4

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

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Step 4.1

Subtract $1$ from both sides of the equation.

$- \frac{7 y}{8} = \frac{9}{4} - 1$

Step 4.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{7 y}{8} = \frac{9}{4} - 1 \cdot \frac{4}{4}$

Step 4.3

Combine $- 1$ and $\frac{4}{4}$ .

$- \frac{7 y}{8} = \frac{9}{4} + \frac{- 1 \cdot 4}{4}$

Step 4.4

Combine the numerators over the common denominator.

$- \frac{7 y}{8} = \frac{9 - 1 \cdot 4}{4}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 1$ by $4$ .

$- \frac{7 y}{8} = \frac{9 - 4}{4}$

Step 4.5.2

Subtract $4$ from $9$ .

$- \frac{7 y}{8} = \frac{5}{4}$

Step 5

Multiply both sides of the equation by $- \frac{8}{7}$ .

$- \frac{8}{7} (- \frac{7 y}{8}) = - \frac{8}{7} \cdot \frac{5}{4}$

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 $- \frac{8}{7} (- \frac{7 y}{8})$ .

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Step 6.1.1.1

Cancel the common factor of $8$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{8}{7}$ into the numerator.

$\frac{- 8}{7} (- \frac{7 y}{8}) = - \frac{8}{7} \cdot \frac{5}{4}$

Step 6.1.1.1.2

Move the leading negative in $- \frac{7 y}{8}$ into the numerator.

$\frac{- 8}{7} \cdot \frac{- 7 y}{8} = - \frac{8}{7} \cdot \frac{5}{4}$

Step 6.1.1.1.3

Factor $8$ out of $- 8$ .

$\frac{8 (- 1)}{7} \cdot \frac{- 7 y}{8} = - \frac{8}{7} \cdot \frac{5}{4}$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{8 \cdot - 1}{7} \cdot \frac{- 7 y}{8} = - \frac{8}{7} \cdot \frac{5}{4}$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{7} (- 7 y) = - \frac{8}{7} \cdot \frac{5}{4}$

Step 6.1.1.2

Cancel the common factor of $7$ .

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Step 6.1.1.2.1

Factor $7$ out of $- 7 y$ .

$\frac{- 1}{7} (7 (- y)) = - \frac{8}{7} \cdot \frac{5}{4}$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{7} (7 (- y)) = - \frac{8}{7} \cdot \frac{5}{4}$

Step 6.1.1.2.3

Rewrite the expression.

$- - y = - \frac{8}{7} \cdot \frac{5}{4}$

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{8}{7} \cdot \frac{5}{4}$

Step 6.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{8}{7} \cdot \frac{5}{4}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{8}{7} \cdot \frac{5}{4}$ .

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Step 6.2.1.1

Cancel the common factor of $4$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{8}{7}$ into the numerator.

$y = \frac{- 8}{7} \cdot \frac{5}{4}$

Step 6.2.1.1.2

Factor $4$ out of $- 8$ .

$y = \frac{4 (- 2)}{7} \cdot \frac{5}{4}$

Step 6.2.1.1.3

Cancel the common factor.

$y = \frac{4 \cdot - 2}{7} \cdot \frac{5}{4}$

Step 6.2.1.1.4

Rewrite the expression.

$y = \frac{- 2}{7} \cdot 5$

Step 6.2.1.2

Combine $\frac{- 2}{7}$ and $5$ .

$y = \frac{- 2 \cdot 5}{7}$

Step 6.2.1.3

Simplify the expression.

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Step 6.2.1.3.1

Multiply $- 2$ by $5$ .

$y = \frac{- 10}{7}$

Step 6.2.1.3.2

Move the negative in front of the fraction.

$y = - \frac{10}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{10}{7}$

Decimal Form:

$y = - 1.\overline{428571}$

Mixed Number Form:

$y = - 1 \frac{3}{7}$