Pre-Algebra Examples

$\frac{3}{4} - 14 y = - 8$

Step 1

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

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Step 1.1

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

$- 14 y = - 8 - \frac{3}{4}$

Step 1.2

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 14 y = - 8 \cdot \frac{4}{4} - \frac{3}{4}$

Step 1.3

Combine $- 8$ and $\frac{4}{4}$ .

$- 14 y = \frac{- 8 \cdot 4}{4} - \frac{3}{4}$

Step 1.4

Combine the numerators over the common denominator.

$- 14 y = \frac{- 8 \cdot 4 - 3}{4}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 8$ by $4$ .

$- 14 y = \frac{- 32 - 3}{4}$

Step 1.5.2

Subtract $3$ from $- 32$ .

$- 14 y = \frac{- 35}{4}$

Step 1.6

Move the negative in front of the fraction.

$- 14 y = - \frac{35}{4}$

Step 2

Divide each term in $- 14 y = - \frac{35}{4}$ by $- 14$ and simplify.

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Step 2.1

Divide each term in $- 14 y = - \frac{35}{4}$ by $- 14$ .

$\frac{- 14 y}{- 14} = \frac{- \frac{35}{4}}{- 14}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 14$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 14 y}{- 14} = \frac{- \frac{35}{4}}{- 14}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- \frac{35}{4}}{- 14}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{35}{4} \cdot \frac{1}{- 14}$

Step 2.3.2

Cancel the common factor of $7$ .

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Step 2.3.2.1

Move the leading negative in $- \frac{35}{4}$ into the numerator.

$y = \frac{- 35}{4} \cdot \frac{1}{- 14}$

Step 2.3.2.2

Factor $7$ out of $- 35$ .

$y = \frac{7 (- 5)}{4} \cdot \frac{1}{- 14}$

Step 2.3.2.3

Factor $7$ out of $- 14$ .

$y = \frac{7 \cdot - 5}{4} \cdot \frac{1}{7 \cdot - 2}$

Step 2.3.2.4

Cancel the common factor.

$y = \frac{7 \cdot - 5}{4} \cdot \frac{1}{7 \cdot - 2}$

Step 2.3.2.5

Rewrite the expression.

$y = \frac{- 5}{4} \cdot \frac{1}{- 2}$

Step 2.3.3

Multiply $\frac{- 5}{4}$ by $\frac{1}{- 2}$ .

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

Step 2.3.4

Multiply $4$ by $- 2$ .

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

Step 2.3.5

Dividing two negative values results in a positive value.

$y = \frac{5}{8}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{5}{8}$

Decimal Form:

$y = 0.625$