Finite Math Examples

$2 - (- 2 \cdot (x - 1) - \frac{x - 3}{2}) = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$2 - (- 2 x - 2 \cdot - 1 - \frac{x - 3}{2}) = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.1.1.2

Multiply $- 2$ by $- 1$ .

$2 - (- 2 x + 2 - \frac{x - 3}{2}) = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.1.2

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

$2 - (- 2 x \cdot \frac{2}{2} - \frac{x - 3}{2} + 2) = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.1.3

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

$2 - (\frac{- 2 x \cdot 2}{2} - \frac{x - 3}{2} + 2) = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.1.4

Combine the numerators over the common denominator.

$2 - (\frac{- 2 x \cdot 2 - (x - 3)}{2} + 2) = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.1.5

Simplify the numerator.

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Step 1.1.5.1

Multiply $2$ by $- 2$ .

$2 - (\frac{- 4 x - (x - 3)}{2} + 2) = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.1.5.2

Apply the distributive property.

$2 - (\frac{- 4 x - x - - 3}{2} + 2) = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.1.5.3

Multiply $- 1$ by $- 3$ .

$2 - (\frac{- 4 x - x + 3}{2} + 2) = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.1.5.4

Subtract $x$ from $- 4 x$ .

$2 - (\frac{- 5 x + 3}{2} + 2) = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.1.6

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

$2 - (\frac{- 5 x + 3}{2} + 2 \cdot \frac{2}{2}) = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.1.7

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

$2 - (\frac{- 5 x + 3}{2} + \frac{2 \cdot 2}{2}) = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.1.8

Combine the numerators over the common denominator.

$2 - \frac{- 5 x + 3 + 2 \cdot 2}{2} = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.1.9

Simplify the numerator.

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Step 1.1.9.1

Multiply $2$ by $2$ .

$2 - \frac{- 5 x + 3 + 4}{2} = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.1.9.2

Add $3$ and $4$ .

$2 - \frac{- 5 x + 7}{2} = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.2

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

$2 \cdot \frac{2}{2} - \frac{- 5 x + 7}{2} = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.3

Simplify terms.

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Step 1.3.1

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

$\frac{2 \cdot 2}{2} - \frac{- 5 x + 7}{2} = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 - (- 5 x + 7)}{2} = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $2$ by $2$ .

$\frac{4 - (- 5 x + 7)}{2} = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.4.2

Apply the distributive property.

$\frac{4 - (- 5 x) - 1 \cdot 7}{2} = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.4.3

Multiply $- 5$ by $- 1$ .

$\frac{4 + 5 x - 1 \cdot 7}{2} = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.4.4

Multiply $- 1$ by $7$ .

$\frac{4 + 5 x - 7}{2} = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 1.4.5

Subtract $7$ from $4$ .

$\frac{5 x - 3}{2} = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3$

Step 2

Simplify $\frac{2 x}{3} - \frac{5 x - 3}{12} + 3$ .

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Step 2.1

Find the common denominator.

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Step 2.1.1

Multiply $\frac{2 x}{3}$ by $\frac{4}{4}$ .

$\frac{5 x - 3}{2} = \frac{2 x}{3} \cdot \frac{4}{4} - \frac{5 x - 3}{12} + 3$

Step 2.1.2

Multiply $\frac{2 x}{3}$ by $\frac{4}{4}$ .

$\frac{5 x - 3}{2} = \frac{2 x \cdot 4}{3 \cdot 4} - \frac{5 x - 3}{12} + 3$

Step 2.1.3

Write $3$ as a fraction with denominator $1$ .

$\frac{5 x - 3}{2} = \frac{2 x \cdot 4}{3 \cdot 4} - \frac{5 x - 3}{12} + \frac{3}{1}$

Step 2.1.4

Multiply $\frac{3}{1}$ by $\frac{12}{12}$ .

$\frac{5 x - 3}{2} = \frac{2 x \cdot 4}{3 \cdot 4} - \frac{5 x - 3}{12} + \frac{3}{1} \cdot \frac{12}{12}$

Step 2.1.5

Multiply $\frac{3}{1}$ by $\frac{12}{12}$ .

$\frac{5 x - 3}{2} = \frac{2 x \cdot 4}{3 \cdot 4} - \frac{5 x - 3}{12} + \frac{3 \cdot 12}{12}$

Step 2.1.6

Multiply $3$ by $4$ .

$\frac{5 x - 3}{2} = \frac{2 x \cdot 4}{12} - \frac{5 x - 3}{12} + \frac{3 \cdot 12}{12}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{5 x - 3}{2} = \frac{2 x \cdot 4 - (5 x - 3) + 3 \cdot 12}{12}$

Step 2.3

Simplify each term.

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Step 2.3.1

Multiply $4$ by $2$ .

$\frac{5 x - 3}{2} = \frac{8 x - (5 x - 3) + 3 \cdot 12}{12}$

Step 2.3.2

Apply the distributive property.

$\frac{5 x - 3}{2} = \frac{8 x - (5 x) - - 3 + 3 \cdot 12}{12}$

Step 2.3.3

Multiply $5$ by $- 1$ .

$\frac{5 x - 3}{2} = \frac{8 x - 5 x - - 3 + 3 \cdot 12}{12}$

Step 2.3.4

Multiply $- 1$ by $- 3$ .

$\frac{5 x - 3}{2} = \frac{8 x - 5 x + 3 + 3 \cdot 12}{12}$

Step 2.3.5

Multiply $3$ by $12$ .

$\frac{5 x - 3}{2} = \frac{8 x - 5 x + 3 + 36}{12}$

Step 2.4

Simplify terms.

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Step 2.4.1

Subtract $5 x$ from $8 x$ .

$\frac{5 x - 3}{2} = \frac{3 x + 3 + 36}{12}$

Step 2.4.2

Add $3$ and $36$ .

$\frac{5 x - 3}{2} = \frac{3 x + 39}{12}$

Step 2.4.3

Cancel the common factor of $3 x + 39$ and $12$ .

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Step 2.4.3.1

Factor $3$ out of $3 x$ .

$\frac{5 x - 3}{2} = \frac{3 (x) + 39}{12}$

Step 2.4.3.2

Factor $3$ out of $39$ .

$\frac{5 x - 3}{2} = \frac{3 x + 3 \cdot 13}{12}$

Step 2.4.3.3

Factor $3$ out of $3 x + 3 \cdot 13$ .

$\frac{5 x - 3}{2} = \frac{3 (x + 13)}{12}$

Step 2.4.3.4

Cancel the common factors.

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Step 2.4.3.4.1

Factor $3$ out of $12$ .

$\frac{5 x - 3}{2} = \frac{3 (x + 13)}{3 (4)}$

Step 2.4.3.4.2

Cancel the common factor.

$\frac{5 x - 3}{2} = \frac{3 (x + 13)}{3 \cdot 4}$

Step 2.4.3.4.3

Rewrite the expression.

$\frac{5 x - 3}{2} = \frac{x + 13}{4}$

Step 3

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

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Step 3.1

Subtract $\frac{x + 13}{4}$ from both sides of the equation.

$\frac{5 x - 3}{2} - \frac{x + 13}{4} = 0$

Step 3.2

To write $\frac{5 x - 3}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x - 3}{2} \cdot \frac{2}{2} - \frac{x + 13}{4} = 0$

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{5 x - 3}{2}$ by $\frac{2}{2}$ .

$\frac{(5 x - 3) \cdot 2}{2 \cdot 2} - \frac{x + 13}{4} = 0$

Step 3.3.2

Multiply $2$ by $2$ .

$\frac{(5 x - 3) \cdot 2}{4} - \frac{x + 13}{4} = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{(5 x - 3) \cdot 2 - (x + 13)}{4} = 0$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Apply the distributive property.

$\frac{5 x \cdot 2 - 3 \cdot 2 - (x + 13)}{4} = 0$

Step 3.5.2

Multiply $2$ by $5$ .

$\frac{10 x - 3 \cdot 2 - (x + 13)}{4} = 0$

Step 3.5.3

Multiply $- 3$ by $2$ .

$\frac{10 x - 6 - (x + 13)}{4} = 0$

Step 3.5.4

Apply the distributive property.

$\frac{10 x - 6 - x - 1 \cdot 13}{4} = 0$

Step 3.5.5

Multiply $- 1$ by $13$ .

$\frac{10 x - 6 - x - 13}{4} = 0$

Step 3.5.6

Subtract $x$ from $10 x$ .

$\frac{9 x - 6 - 13}{4} = 0$

Step 3.5.7

Subtract $13$ from $- 6$ .

$\frac{9 x - 19}{4} = 0$

Step 4

Set the numerator equal to zero.

$9 x - 19 = 0$

Step 5

Solve the equation for $x$ .

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Step 5.1

Add $19$ to both sides of the equation.

$9 x = 19$

Step 5.2

Divide each term in $9 x = 19$ by $9$ and simplify.

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Step 5.2.1

Divide each term in $9 x = 19$ by $9$ .

$\frac{9 x}{9} = \frac{19}{9}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $9$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{19}{9}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{19}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{19}{9}$

Decimal Form:

$x = 2.\overline{1}$

Mixed Number Form:

$x = 2 \frac{1}{9}$