Algebra Examples

$\frac{4}{6} (x + \frac{1}{2} + 4) = \frac{1}{6} (x + 2)$

Step 1

Simplify $\frac{4}{6} \cdot (x + \frac{1}{2} + 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{4}{6} \cdot (x + \frac{1}{2} + 4) = \frac{1}{6} \cdot (x + 2)$

Step 1.2

Simplify by adding zeros.

$\frac{4}{6} \cdot (x + \frac{1}{2} + 4) = \frac{1}{6} \cdot (x + 2)$

Step 1.3

Cancel the common factor of $4$ and $6$ .

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Step 1.3.1

Factor $2$ out of $4$ .

$\frac{2 (2)}{6} \cdot (x + \frac{1}{2} + 4) = \frac{1}{6} \cdot (x + 2)$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 2}{2 \cdot 3} \cdot (x + \frac{1}{2} + 4) = \frac{1}{6} \cdot (x + 2)$

Step 1.3.2.2

Cancel the common factor.

$\frac{2 \cdot 2}{2 \cdot 3} \cdot (x + \frac{1}{2} + 4) = \frac{1}{6} \cdot (x + 2)$

Step 1.3.2.3

Rewrite the expression.

$\frac{2}{3} \cdot (x + \frac{1}{2} + 4) = \frac{1}{6} \cdot (x + 2)$

Step 1.4

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2}{3} \cdot (x + \frac{1}{2} + 4 \cdot \frac{2}{2}) = \frac{1}{6} \cdot (x + 2)$

Step 1.5

Combine $4$ and $\frac{2}{2}$ .

$\frac{2}{3} \cdot (x + \frac{1}{2} + \frac{4 \cdot 2}{2}) = \frac{1}{6} \cdot (x + 2)$

Step 1.6

Combine the numerators over the common denominator.

$\frac{2}{3} \cdot (x + \frac{1 + 4 \cdot 2}{2}) = \frac{1}{6} \cdot (x + 2)$

Step 1.7

Simplify the numerator.

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Step 1.7.1

Multiply $4$ by $2$ .

$\frac{2}{3} \cdot (x + \frac{1 + 8}{2}) = \frac{1}{6} \cdot (x + 2)$

Step 1.7.2

Add $1$ and $8$ .

$\frac{2}{3} \cdot (x + \frac{9}{2}) = \frac{1}{6} \cdot (x + 2)$

Step 1.8

Apply the distributive property.

$\frac{2}{3} x + \frac{2}{3} \cdot \frac{9}{2} = \frac{1}{6} \cdot (x + 2)$

Step 1.9

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

$\frac{2 x}{3} + \frac{2}{3} \cdot \frac{9}{2} = \frac{1}{6} \cdot (x + 2)$

Step 1.10

Cancel the common factor of $2$ .

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Step 1.10.1

Cancel the common factor.

$\frac{2 x}{3} + \frac{2}{3} \cdot \frac{9}{2} = \frac{1}{6} \cdot (x + 2)$

Step 1.10.2

Rewrite the expression.

$\frac{2 x}{3} + \frac{1}{3} \cdot 9 = \frac{1}{6} \cdot (x + 2)$

Step 1.11

Cancel the common factor of $3$ .

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Step 1.11.1

Factor $3$ out of $9$ .

$\frac{2 x}{3} + \frac{1}{3} \cdot (3 (3)) = \frac{1}{6} \cdot (x + 2)$

Step 1.11.2

Cancel the common factor.

$\frac{2 x}{3} + \frac{1}{3} \cdot (3 \cdot 3) = \frac{1}{6} \cdot (x + 2)$

Step 1.11.3

Rewrite the expression.

$\frac{2 x}{3} + 3 = \frac{1}{6} \cdot (x + 2)$

Step 2

Simplify $\frac{1}{6} \cdot (x + 2)$ .

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Step 2.1

Apply the distributive property.

$\frac{2 x}{3} + 3 = \frac{1}{6} x + \frac{1}{6} \cdot 2$

Step 2.2

Combine $\frac{1}{6}$ and $x$ .

$\frac{2 x}{3} + 3 = \frac{x}{6} + \frac{1}{6} \cdot 2$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $6$ .

$\frac{2 x}{3} + 3 = \frac{x}{6} + \frac{1}{2 (3)} \cdot 2$

Step 2.3.2

Cancel the common factor.

$\frac{2 x}{3} + 3 = \frac{x}{6} + \frac{1}{2 \cdot 3} \cdot 2$

Step 2.3.3

Rewrite the expression.

$\frac{2 x}{3} + 3 = \frac{x}{6} + \frac{1}{3}$

Step 3

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

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Step 3.1

Subtract $\frac{x}{6}$ from both sides of the equation.

$\frac{2 x}{3} + 3 - \frac{x}{6} = \frac{1}{3}$

Step 3.2

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

$\frac{2 x}{3} \cdot \frac{2}{2} - \frac{x}{6} + 3 = \frac{1}{3}$

Step 3.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{2 x}{3}$ by $\frac{2}{2}$ .

$\frac{2 x \cdot 2}{3 \cdot 2} - \frac{x}{6} + 3 = \frac{1}{3}$

Step 3.3.2

Multiply $3$ by $2$ .

$\frac{2 x \cdot 2}{6} - \frac{x}{6} + 3 = \frac{1}{3}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{2 x \cdot 2 - x}{6} + 3 = \frac{1}{3}$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $x$ out of $2 x \cdot 2 - x$ .

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Step 3.5.1.1.1

Factor $x$ out of $2 x \cdot 2$ .

$\frac{x (2 \cdot 2) - x}{6} + 3 = \frac{1}{3}$

Step 3.5.1.1.2

Factor $x$ out of $- x$ .

$\frac{x (2 \cdot 2) + x \cdot - 1}{6} + 3 = \frac{1}{3}$

Step 3.5.1.1.3

Factor $x$ out of $x (2 \cdot 2) + x \cdot - 1$ .

$\frac{x (2 \cdot 2 - 1)}{6} + 3 = \frac{1}{3}$

Step 3.5.1.2

Multiply $2$ by $2$ .

$\frac{x (4 - 1)}{6} + 3 = \frac{1}{3}$

Step 3.5.1.3

Subtract $1$ from $4$ .

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

Step 3.5.2

Cancel the common factor of $3$ and $6$ .

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Step 3.5.2.1

Factor $3$ out of $x \cdot 3$ .

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

Step 3.5.2.2

Cancel the common factors.

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Step 3.5.2.2.1

Factor $3$ out of $6$ .

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

Step 3.5.2.2.2

Cancel the common factor.

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

Step 3.5.2.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

Subtract $3$ from both sides of the equation.

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 3$ by $3$ .

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

Step 4.5.2

Subtract $9$ from $1$ .

$\frac{x}{2} = \frac{- 8}{3}$

Step 4.6

Move the negative in front of the fraction.

$\frac{x}{2} = - \frac{8}{3}$

Step 5

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 (- \frac{8}{3})$

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

Cancel the common factor of $2$ .

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Step 6.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 (- \frac{8}{3})$

Step 6.1.1.2

Rewrite the expression.

$x = 2 (- \frac{8}{3})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $2 (- \frac{8}{3})$ .

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Step 6.2.1.1

Multiply $2 (- \frac{8}{3})$ .

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Step 6.2.1.1.1

Multiply $- 1$ by $2$ .

$x = - 2 (\frac{8}{3})$

Step 6.2.1.1.2

Combine $- 2$ and $\frac{8}{3}$ .

$x = \frac{- 2 \cdot 8}{3}$

Step 6.2.1.1.3

Multiply $- 2$ by $8$ .

$x = \frac{- 16}{3}$

Step 6.2.1.2

Move the negative in front of the fraction.

$x = - \frac{16}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{16}{3}$

Decimal Form:

$x = - 5.\overline{3}$

Mixed Number Form:

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