Finite Math Examples

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

Step 1

Multiply both sides by $2$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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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.

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

Step 2.1.1.1.2

Multiply $3$ by $1$ .

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

Step 2.1.1.1.3

Multiply $- 1$ by $3$ .

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

Step 2.1.1.2

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

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

Step 2.1.1.3

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

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

Step 2.1.1.4

Combine the numerators over the common denominator.

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

Step 2.1.1.5

Simplify the numerator.

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Step 2.1.1.5.1

Multiply $3$ by $3$ .

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

Step 2.1.1.5.2

Subtract $1$ from $9$ .

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

Step 2.1.1.6

Apply the distributive property.

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

Step 2.1.1.7

Multiply $2$ by $- 3$ .

$- 6 x + \frac{8}{3} \cdot 2 = \frac{2 - 3 x}{2} \cdot 2$

Step 2.1.1.8

Multiply $\frac{8}{3} \cdot 2$ .

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Step 2.1.1.8.1

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

$- 6 x + \frac{8 \cdot 2}{3} = \frac{2 - 3 x}{2} \cdot 2$

Step 2.1.1.8.2

Multiply $8$ by $2$ .

$- 6 x + \frac{16}{3} = \frac{2 - 3 x}{2} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Cancel the common factor.

$- 6 x + \frac{16}{3} = \frac{2 - 3 x}{2} \cdot 2$

Step 2.2.1.1.2

Rewrite the expression.

$- 6 x + \frac{16}{3} = 2 - 3 x$

Step 2.2.1.2

Reorder $2$ and $- 3 x$ .

$- 6 x + \frac{16}{3} = - 3 x + 2$

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

Add $3 x$ to both sides of the equation.

$- 6 x + \frac{16}{3} + 3 x = 2$

Step 3.1.2

Add $- 6 x$ and $3 x$ .

$- 3 x + \frac{16}{3} = 2$

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 $\frac{16}{3}$ from both sides of the equation.

$- 3 x = 2 - \frac{16}{3}$

Step 3.2.2

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

$- 3 x = 2 \cdot \frac{3}{3} - \frac{16}{3}$

Step 3.2.3

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

$- 3 x = \frac{2 \cdot 3}{3} - \frac{16}{3}$

Step 3.2.4

Combine the numerators over the common denominator.

$- 3 x = \frac{2 \cdot 3 - 16}{3}$

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply $2$ by $3$ .

$- 3 x = \frac{6 - 16}{3}$

Step 3.2.5.2

Subtract $16$ from $6$ .

$- 3 x = \frac{- 10}{3}$

Step 3.2.6

Move the negative in front of the fraction.

$- 3 x = - \frac{10}{3}$

Step 3.3

Divide each term in $- 3 x = - \frac{10}{3}$ by $- 3$ and simplify.

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Step 3.3.1

Divide each term in $- 3 x = - \frac{10}{3}$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- \frac{10}{3}}{- 3}$

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.

$\frac{- 3 x}{- 3} = \frac{- \frac{10}{3}}{- 3}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{10}{3}}{- 3}$

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.

$x = - \frac{10}{3} \cdot \frac{1}{- 3}$

Step 3.3.3.2

Move the negative in front of the fraction.

$x = - \frac{10}{3} (- \frac{1}{3})$

Step 3.3.3.3

Multiply $- \frac{10}{3} (- \frac{1}{3})$ .

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Step 3.3.3.3.1

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{10}{3}) \frac{1}{3}$

Step 3.3.3.3.2

Multiply $\frac{10}{3}$ by $1$ .

$x = \frac{10}{3} \cdot \frac{1}{3}$

Step 3.3.3.3.3

Multiply $\frac{10}{3}$ by $\frac{1}{3}$ .

$x = \frac{10}{3 \cdot 3}$

Step 3.3.3.3.4

Multiply $3$ by $3$ .

$x = \frac{10}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{10}{9}$

Decimal Form:

$x = 1.\overline{1}$

Mixed Number Form:

$x = 1 \frac{1}{9}$