Finite Math Examples

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

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{1}{2} - \frac{x}{3}) \cdot 3$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Combine $\frac{1}{2}$ and $3$ .

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

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

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

Step 2.1.1.3.2

Cancel the common factor.

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

Step 2.1.1.3.3

Rewrite the expression.

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

Step 2.1.1.4

Reorder $\frac{3}{2}$ and $- x$ .

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

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

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 $2 x$ from both sides of the equation.

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

Step 3.1.2

Subtract $2 x$ from $- x$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.2.3

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

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

Step 3.2.4

Combine the numerators over the common denominator.

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

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply $- 3$ by $2$ .

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

Step 3.2.5.2

Subtract $3$ from $- 6$ .

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

Step 3.2.6

Move the negative in front of the fraction.

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

Step 3.3

Divide each term in $- 3 x = - \frac{9}{2}$ by $- 3$ and simplify.

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Step 3.3.1

Divide each term in $- 3 x = - \frac{9}{2}$ by $- 3$ .

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

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 3$ .

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Step 3.3.2.1.1

Cancel the common factor.

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

Step 3.3.2.1.2

Divide $x$ by $1$ .

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

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.3.3.2

Cancel the common factor of $3$ .

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Step 3.3.3.2.1

Move the leading negative in $- \frac{9}{2}$ into the numerator.

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

Step 3.3.3.2.2

Factor $3$ out of $- 9$ .

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

Step 3.3.3.2.3

Factor $3$ out of $- 3$ .

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

Step 3.3.3.2.4

Cancel the common factor.

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

Step 3.3.3.2.5

Rewrite the expression.

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

Step 3.3.3.3

Multiply $\frac{- 3}{2}$ by $\frac{1}{- 1}$ .

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

Step 3.3.3.4

Multiply $2$ by $- 1$ .

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

Step 3.3.3.5

Dividing two negative values results in a positive value.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5$

Mixed Number Form:

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