Algebra Examples

$8 \frac{1}{3} - x = 5 \frac{1}{4} - 14 \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

Convert $8 \frac{1}{3}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$8 + \frac{1}{3} - x = 5 \frac{1}{4} - 14 \frac{1}{2}$

Step 1.1.2

Add $8$ and $\frac{1}{3}$ .

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Step 1.1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$8 \cdot \frac{3}{3} + \frac{1}{3} - x = 5 \frac{1}{4} - 14 \frac{1}{2}$

Step 1.1.2.2

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

$\frac{8 \cdot 3}{3} + \frac{1}{3} - x = 5 \frac{1}{4} - 14 \frac{1}{2}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 3 + 1}{3} - x = 5 \frac{1}{4} - 14 \frac{1}{2}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $8$ by $3$ .

$\frac{24 + 1}{3} - x = 5 \frac{1}{4} - 14 \frac{1}{2}$

Step 1.1.2.4.2

Add $24$ and $1$ .

$\frac{25}{3} - x = 5 \frac{1}{4} - 14 \frac{1}{2}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $5 \frac{1}{4} - 14 \frac{1}{2}$ .

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Step 2.1.1

Convert $5 \frac{1}{4}$ to an improper fraction.

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Step 2.1.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{25}{3} - x = 5 + \frac{1}{4} - 14 \frac{1}{2}$

Step 2.1.1.2

Add $5$ and $\frac{1}{4}$ .

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Step 2.1.1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{25}{3} - x = 5 \cdot \frac{4}{4} + \frac{1}{4} - 14 \frac{1}{2}$

Step 2.1.1.2.2

Combine $5$ and $\frac{4}{4}$ .

$\frac{25}{3} - x = \frac{5 \cdot 4}{4} + \frac{1}{4} - 14 \frac{1}{2}$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$\frac{25}{3} - x = \frac{5 \cdot 4 + 1}{4} - 14 \frac{1}{2}$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $5$ by $4$ .

$\frac{25}{3} - x = \frac{20 + 1}{4} - 14 \frac{1}{2}$

Step 2.1.1.2.4.2

Add $20$ and $1$ .

$\frac{25}{3} - x = \frac{21}{4} - 14 \frac{1}{2}$

Step 2.1.2

Convert $14 \frac{1}{2}$ to an improper fraction.

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Step 2.1.2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{25}{3} - x = \frac{21}{4} - (14 + \frac{1}{2})$

Step 2.1.2.2

Add $14$ and $\frac{1}{2}$ .

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Step 2.1.2.2.1

To write $14$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{25}{3} - x = \frac{21}{4} - (14 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.1.2.2.2

Combine $14$ and $\frac{2}{2}$ .

$\frac{25}{3} - x = \frac{21}{4} - (\frac{14 \cdot 2}{2} + \frac{1}{2})$

Step 2.1.2.2.3

Combine the numerators over the common denominator.

$\frac{25}{3} - x = \frac{21}{4} - \frac{14 \cdot 2 + 1}{2}$

Step 2.1.2.2.4

Simplify the numerator.

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Step 2.1.2.2.4.1

Multiply $14$ by $2$ .

$\frac{25}{3} - x = \frac{21}{4} - \frac{28 + 1}{2}$

Step 2.1.2.2.4.2

Add $28$ and $1$ .

$\frac{25}{3} - x = \frac{21}{4} - \frac{29}{2}$

Step 2.1.3

To write $- \frac{29}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{25}{3} - x = \frac{21}{4} - \frac{29}{2} \cdot \frac{2}{2}$

Step 2.1.4

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

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Step 2.1.4.1

Multiply $\frac{29}{2}$ by $\frac{2}{2}$ .

$\frac{25}{3} - x = \frac{21}{4} - \frac{29 \cdot 2}{2 \cdot 2}$

Step 2.1.4.2

Multiply $2$ by $2$ .

$\frac{25}{3} - x = \frac{21}{4} - \frac{29 \cdot 2}{4}$

Step 2.1.5

Combine the numerators over the common denominator.

$\frac{25}{3} - x = \frac{21 - 29 \cdot 2}{4}$

Step 2.1.6

Simplify the numerator.

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Step 2.1.6.1

Multiply $- 29$ by $2$ .

$\frac{25}{3} - x = \frac{21 - 58}{4}$

Step 2.1.6.2

Subtract $58$ from $21$ .

$\frac{25}{3} - x = \frac{- 37}{4}$

Step 2.1.7

Move the negative in front of the fraction.

$\frac{25}{3} - x = - \frac{37}{4}$

Step 3

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

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Step 3.1

Subtract $\frac{25}{3}$ from both sides of the equation.

$- x = - \frac{37}{4} - \frac{25}{3}$

Step 3.2

To write $- \frac{37}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- x = - \frac{37}{4} \cdot \frac{3}{3} - \frac{25}{3}$

Step 3.3

To write $- \frac{25}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- x = - \frac{37}{4} \cdot \frac{3}{3} - \frac{25}{3} \cdot \frac{4}{4}$

Step 3.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{37}{4}$ by $\frac{3}{3}$ .

$- x = - \frac{37 \cdot 3}{4 \cdot 3} - \frac{25}{3} \cdot \frac{4}{4}$

Step 3.4.2

Multiply $4$ by $3$ .

$- x = - \frac{37 \cdot 3}{12} - \frac{25}{3} \cdot \frac{4}{4}$

Step 3.4.3

Multiply $\frac{25}{3}$ by $\frac{4}{4}$ .

$- x = - \frac{37 \cdot 3}{12} - \frac{25 \cdot 4}{3 \cdot 4}$

Step 3.4.4

Multiply $3$ by $4$ .

$- x = - \frac{37 \cdot 3}{12} - \frac{25 \cdot 4}{12}$

Step 3.5

Combine the numerators over the common denominator.

$- x = \frac{- 37 \cdot 3 - 25 \cdot 4}{12}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $- 37$ by $3$ .

$- x = \frac{- 111 - 25 \cdot 4}{12}$

Step 3.6.2

Multiply $- 25$ by $4$ .

$- x = \frac{- 111 - 100}{12}$

Step 3.6.3

Subtract $100$ from $- 111$ .

$- x = \frac{- 211}{12}$

Step 3.7

Move the negative in front of the fraction.

$- x = - \frac{211}{12}$

Step 4

Divide each term in $- x = - \frac{211}{12}$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- x = - \frac{211}{12}$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- \frac{211}{12}}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- \frac{211}{12}}{- 1}$

Step 4.2.2

Divide $x$ by $1$ .

$x = \frac{- \frac{211}{12}}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

$x = \frac{\frac{211}{12}}{1}$

Step 4.3.2

Divide $\frac{211}{12}$ by $1$ .

$x = \frac{211}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{211}{12}$

Decimal Form:

$x = 17.58\overline{3}$

Mixed Number Form:

$x = 17 \frac{7}{12}$