Pre-Algebra Examples

$- \frac{1}{3} \cdot (x - 9) = - 1$

Step 1

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

$- 3 (- \frac{1}{3} \cdot (x - 9)) = - 3 \cdot - 1$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $- 3 (- \frac{1}{3} \cdot (x - 9))$ .

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Step 2.1.1.1

Apply the distributive property.

$- 3 (- \frac{1}{3} x - \frac{1}{3} \cdot - 9) = - 3 \cdot - 1$

Step 2.1.1.2

Combine $x$ and $\frac{1}{3}$ .

$- 3 (- \frac{x}{3} - \frac{1}{3} \cdot - 9) = - 3 \cdot - 1$

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$- 3 (- \frac{x}{3} + \frac{- 1}{3} \cdot - 9) = - 3 \cdot - 1$

Step 2.1.1.3.2

Factor $3$ out of $- 9$ .

$- 3 (- \frac{x}{3} + \frac{- 1}{3} \cdot (3 (- 3))) = - 3 \cdot - 1$

Step 2.1.1.3.3

Cancel the common factor.

$- 3 (- \frac{x}{3} + \frac{- 1}{3} \cdot (3 \cdot - 3)) = - 3 \cdot - 1$

Step 2.1.1.3.4

Rewrite the expression.

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

Step 2.1.1.4

Multiply $- 1$ by $- 3$ .

$- 3 (- \frac{x}{3} + 3) = - 3 \cdot - 1$

Step 2.1.1.5

Apply the distributive property.

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

Step 2.1.1.6

Cancel the common factor of $3$ .

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Step 2.1.1.6.1

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

$- 3 \frac{- x}{3} - 3 \cdot 3 = - 3 \cdot - 1$

Step 2.1.1.6.2

Factor $3$ out of $- 3$ .

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

Step 2.1.1.6.3

Cancel the common factor.

$3 \cdot - 1 \frac{- x}{3} - 3 \cdot 3 = - 3 \cdot - 1$

Step 2.1.1.6.4

Rewrite the expression.

$- - x - 3 \cdot 3 = - 3 \cdot - 1$

Step 2.1.1.7

Multiply.

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Step 2.1.1.7.1

Multiply $- 1$ by $- 1$ .

$1 x - 3 \cdot 3 = - 3 \cdot - 1$

Step 2.1.1.7.2

Multiply $x$ by $1$ .

$x - 3 \cdot 3 = - 3 \cdot - 1$

Step 2.1.1.7.3

Multiply $- 3$ by $3$ .

$x - 9 = - 3 \cdot - 1$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 3$ by $- 1$ .

$x - 9 = 3$

Step 3

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

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Step 3.1

Add $9$ to both sides of the equation.

$x = 3 + 9$

Step 3.2

Add $3$ and $9$ .

$x = 12$