Algebra Examples

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

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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Step 2.2.1.1

Simplify terms.

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Step 2.2.1.1.1

Apply the distributive property.

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

Step 2.2.1.1.2

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

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

Step 2.2.1.1.3

Multiply $- 2$ by $3$ .

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

Step 2.2.1.2

Move $3$ to the left of $x$ .

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

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $\frac{3 x}{2}$ from both sides of the equation.

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

Step 3.1.2

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

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

Step 3.1.3

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

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

Step 3.1.4

Combine the numerators over the common denominator.

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

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

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

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

Step 3.1.5.2

Subtract $3 x$ from $2 x$ .

$\frac{- x}{2} = - 6$

Step 3.1.6

Move the negative in front of the fraction.

$- \frac{x}{2} = - 6$

Step 3.2

Multiply both sides of the equation by $- 2$ .

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

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

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

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Step 3.3.1.1.1

Cancel the common factor of $2$ .

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Step 3.3.1.1.1.1

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

$- 2 \frac{- x}{2} = - 2 \cdot - 6$

Step 3.3.1.1.1.2

Factor $2$ out of $- 2$ .

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

Step 3.3.1.1.1.3

Cancel the common factor.

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

Step 3.3.1.1.1.4

Rewrite the expression.

$- - x = - 2 \cdot - 6$

Step 3.3.1.1.2

Multiply.

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Step 3.3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot - 6$

Step 3.3.1.1.2.2

Multiply $x$ by $1$ .

$x = - 2 \cdot - 6$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Multiply $- 2$ by $- 6$ .

$x = 12$