Algebra Examples

$\frac{1}{3} x = x + 8$

Step 1

Simplify $\frac{1}{3} x$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{3} x = x + 8$

Step 1.2

Simplify by adding zeros.

$\frac{1}{3} x = x + 8$

Step 1.3

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

$\frac{x}{3} = x + 8$

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

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

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Step 2.5.1.1

Raise $x$ to the power of $1$ .

$\frac{x^{1} - x \cdot 3}{3} = 8$

Step 2.5.1.2

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - x \cdot 3}{3} = 8$

Step 2.5.1.3

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

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

Step 2.5.1.4

Factor $x$ out of $x \cdot 1 + x (- 1 \cdot 3)$ .

$\frac{x (1 - 1 \cdot 3)}{3} = 8$

Step 2.5.2

Multiply $- 1$ by $3$ .

$\frac{x (1 - 3)}{3} = 8$

Step 2.5.3

Subtract $3$ from $1$ .

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

Step 2.6

Move $- 2$ to the left of $x$ .

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

Step 2.7

Move the negative in front of the fraction.

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

Step 3

Multiply both sides of the equation by $- \frac{3}{2}$ .

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

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 $- \frac{3}{2} (- \frac{2 x}{3})$ .

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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 $- \frac{3}{2}$ into the numerator.

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

Step 4.1.1.1.2

Move the leading negative in $- \frac{2 x}{3}$ into the numerator.

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

Step 4.1.1.1.3

Factor $3$ out of $- 3$ .

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

Step 4.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{- 2 x}{3} = - \frac{3}{2} \cdot 8$

Step 4.1.1.1.5

Rewrite the expression.

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

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

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

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

Step 4.1.1.2.2

Cancel the common factor.

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

Step 4.1.1.2.3

Rewrite the expression.

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

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{2} \cdot 8$

Step 4.1.1.3.2

Multiply $x$ by $1$ .

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{3}{2} \cdot 8$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Step 4.2.1.1.2

Factor $2$ out of $8$ .

$x = \frac{- 3}{2} \cdot (2 (4))$

Step 4.2.1.1.3

Cancel the common factor.

$x = \frac{- 3}{2} \cdot (2 \cdot 4)$

Step 4.2.1.1.4

Rewrite the expression.

$x = - 3 \cdot 4$

Step 4.2.1.2

Multiply $- 3$ by $4$ .

$x = - 12$