Algebra Examples

$\frac{1}{3} (x - 6) = \frac{1}{9} x - \frac{5}{3}$

Step 1

Simplify $\frac{1}{3} \cdot (x - 6)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{3} \cdot (x - 6) = \frac{1}{9} x - \frac{5}{3}$

Step 1.2

Simplify by adding zeros.

$\frac{1}{3} \cdot (x - 6) = \frac{1}{9} x - \frac{5}{3}$

Step 1.3

Apply the distributive property.

$\frac{1}{3} x + \frac{1}{3} \cdot - 6 = \frac{1}{9} x - \frac{5}{3}$

Step 1.4

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

$\frac{x}{3} + \frac{1}{3} \cdot - 6 = \frac{1}{9} x - \frac{5}{3}$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $- 6$ .

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

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

Rewrite the expression.

$\frac{x}{3} - 2 = \frac{1}{9} x - \frac{5}{3}$

Step 2

Combine $\frac{1}{9}$ and $x$ .

$\frac{x}{3} - 2 = \frac{x}{9} - \frac{5}{3}$

Step 3

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

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Step 3.1

Subtract $\frac{x}{9}$ from both sides of the equation.

$\frac{x}{3} - 2 - \frac{x}{9} = - \frac{5}{3}$

Step 3.2

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{3} \cdot \frac{3}{3} - \frac{x}{9} - 2 = - \frac{5}{3}$

Step 3.3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{x}{3}$ by $\frac{3}{3}$ .

$\frac{x \cdot 3}{3 \cdot 3} - \frac{x}{9} - 2 = - \frac{5}{3}$

Step 3.3.2

Multiply $3$ by $3$ .

$\frac{x \cdot 3}{9} - \frac{x}{9} - 2 = - \frac{5}{3}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{x \cdot 3 - x}{9} - 2 = - \frac{5}{3}$

Step 3.5

Subtract $x$ from $x \cdot 3$ .

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Step 3.5.1

Reorder $x$ and $3$ .

$\frac{3 \cdot x - x}{9} - 2 = - \frac{5}{3}$

Step 3.5.2

Subtract $x$ from $3 \cdot x$ .

$\frac{2 \cdot x}{9} - 2 = - \frac{5}{3}$

$\frac{2 x}{9} - 2 = - \frac{5}{3}$

Step 4

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

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Step 4.1

Add $2$ to both sides of the equation.

$\frac{2 x}{9} = - \frac{5}{3} + 2$

Step 4.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x}{9} = - \frac{5}{3} + 2 \cdot \frac{3}{3}$

Step 4.3

Combine $2$ and $\frac{3}{3}$ .

$\frac{2 x}{9} = - \frac{5}{3} + \frac{2 \cdot 3}{3}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{2 x}{9} = \frac{- 5 + 2 \cdot 3}{3}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $2$ by $3$ .

$\frac{2 x}{9} = \frac{- 5 + 6}{3}$

Step 4.5.2

Add $- 5$ and $6$ .

$\frac{2 x}{9} = \frac{1}{3}$

Step 5

Multiply both sides of the equation by $\frac{9}{2}$ .

$\frac{9}{2} \cdot \frac{2 x}{9} = \frac{9}{2} \cdot \frac{1}{3}$

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 $\frac{9}{2} \cdot \frac{2 x}{9}$ .

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Step 6.1.1.1

Cancel the common factor of $9$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{9}{2} \cdot \frac{2 x}{9} = \frac{9}{2} \cdot \frac{1}{3}$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{9}{2} \cdot \frac{1}{3}$

Step 6.1.1.2

Cancel the common factor of $2$ .

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Step 6.1.1.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{9}{2} \cdot \frac{1}{3}$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{9}{2} \cdot \frac{1}{3}$

Step 6.1.1.2.3

Rewrite the expression.

$x = \frac{9}{2} \cdot \frac{1}{3}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Cancel the common factor of $3$ .

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Step 6.2.1.1

Factor $3$ out of $9$ .

$x = \frac{3 (3)}{2} \cdot \frac{1}{3}$

Step 6.2.1.2

Cancel the common factor.

$x = \frac{3 \cdot 3}{2} \cdot \frac{1}{3}$

Step 6.2.1.3

Rewrite the expression.

$x = \frac{3}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$