Basic Math Examples

$5 = 9 - \frac{3}{7 y}$

Step 1

Rewrite the equation as $9 - \frac{3}{7 y} = 5$ .

$9 - \frac{3}{7 y} = 5$

Step 2

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

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Step 2.1

Subtract $9$ from both sides of the equation.

$- \frac{3}{7 y} = 5 - 9$

Step 2.2

Subtract $9$ from $5$ .

$- \frac{3}{7 y} = - 4$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$7 y, 1$

Step 3.2

The LCM of one and any expression is the expression.

$7 y$

Step 4

Multiply each term in $- \frac{3}{7 y} = - 4$ by $7 y$ to eliminate the fractions.

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Step 4.1

Multiply each term in $- \frac{3}{7 y} = - 4$ by $7 y$ .

$- \frac{3}{7 y} (7 y) = - 4 (7 y)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $7 y$ .

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Step 4.2.1.1

Move the leading negative in $- \frac{3}{7 y}$ into the numerator.

$\frac{- 3}{7 y} (7 y) = - 4 (7 y)$

Step 4.2.1.2

Cancel the common factor.

$\frac{- 3}{7 y} (7 y) = - 4 (7 y)$

Step 4.2.1.3

Rewrite the expression.

$- 3 = - 4 (7 y)$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply $7$ by $- 4$ .

$- 3 = - 28 y$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $- 28 y = - 3$ .

$- 28 y = - 3$

Step 5.2

Divide each term in $- 28 y = - 3$ by $- 28$ and simplify.

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Step 5.2.1

Divide each term in $- 28 y = - 3$ by $- 28$ .

$\frac{- 28 y}{- 28} = \frac{- 3}{- 28}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $- 28$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{- 28 y}{- 28} = \frac{- 3}{- 28}$

Step 5.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 3}{- 28}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Dividing two negative values results in a positive value.

$y = \frac{3}{28}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{3}{28}$

Decimal Form:

$y = 0.10714285 \dots$