Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Subtract $5$ from both sides of the equation.

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

Step 2.2

Subtract $5$ from $9$ .

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

Step 3

Multiply both sides of the equation by $- 3$ .

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- 3 (- \frac{y}{3})$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

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

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

Step 4.1.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- y}{3} = - 3 \cdot 4$

Step 4.1.1.1.3

Cancel the common factor.

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

Step 4.1.1.1.4

Rewrite the expression.

$- - y = - 3 \cdot 4$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 3 \cdot 4$

Step 4.1.1.2.2

Multiply $y$ by $1$ .

$y = - 3 \cdot 4$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 3$ by $4$ .

$y = - 12$