Finite Math Examples

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

Step 1

Multiply both sides by $2$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

Simplify each term.

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Step 2.1.1.1.1

Apply the distributive property.

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

Step 2.1.1.1.2

Multiply $- 2 (- \frac{1}{3})$ .

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Step 2.1.1.1.2.1

Multiply $- 1$ by $- 2$ .

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

Step 2.1.1.1.2.2

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

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

Step 2.1.1.2

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

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

Step 2.1.1.3

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

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

Step 2.1.1.4

Combine the numerators over the common denominator.

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

Step 2.1.1.5

Simplify the numerator.

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Step 2.1.1.5.1

Multiply $3$ by $3$ .

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

Step 2.1.1.5.2

Add $9$ and $2$ .

$(- 2 x + \frac{11}{3}) \cdot 2 = \frac{x}{2} \cdot 2$

Step 2.1.1.6

Apply the distributive property.

$- 2 x \cdot 2 + \frac{11}{3} \cdot 2 = \frac{x}{2} \cdot 2$

Step 2.1.1.7

Multiply $2$ by $- 2$ .

$- 4 x + \frac{11}{3} \cdot 2 = \frac{x}{2} \cdot 2$

Step 2.1.1.8

Multiply $\frac{11}{3} \cdot 2$ .

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Step 2.1.1.8.1

Combine $\frac{11}{3}$ and $2$ .

$- 4 x + \frac{11 \cdot 2}{3} = \frac{x}{2} \cdot 2$

Step 2.1.1.8.2

Multiply $11$ by $2$ .

$- 4 x + \frac{22}{3} = \frac{x}{2} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$- 4 x + \frac{22}{3} = \frac{x}{2} \cdot 2$

Step 2.2.1.2

Rewrite the expression.

$- 4 x + \frac{22}{3} = x$

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 $x$ from both sides of the equation.

$- 4 x + \frac{22}{3} - x = 0$

Step 3.1.2

Subtract $x$ from $- 4 x$ .

$- 5 x + \frac{22}{3} = 0$

Step 3.2

Subtract $\frac{22}{3}$ from both sides of the equation.

$- 5 x = - \frac{22}{3}$

Step 3.3

Divide each term in $- 5 x = - \frac{22}{3}$ by $- 5$ and simplify.

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Step 3.3.1

Divide each term in $- 5 x = - \frac{22}{3}$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- \frac{22}{3}}{- 5}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 5$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- \frac{22}{3}}{- 5}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{22}{3}}{- 5}$

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.

$x = - \frac{22}{3} \cdot \frac{1}{- 5}$

Step 3.3.3.2

Move the negative in front of the fraction.

$x = - \frac{22}{3} (- \frac{1}{5})$

Step 3.3.3.3

Multiply $- \frac{22}{3} (- \frac{1}{5})$ .

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Step 3.3.3.3.1

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{22}{3}) \frac{1}{5}$

Step 3.3.3.3.2

Multiply $\frac{22}{3}$ by $1$ .

$x = \frac{22}{3} \cdot \frac{1}{5}$

Step 3.3.3.3.3

Multiply $\frac{22}{3}$ by $\frac{1}{5}$ .

$x = \frac{22}{3 \cdot 5}$

Step 3.3.3.3.4

Multiply $3$ by $5$ .

$x = \frac{22}{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{22}{15}$

Decimal Form:

$x = 1.4\overline{6}$

Mixed Number Form:

$x = 1 \frac{7}{15}$