Basic Math Examples

$\frac{9 \frac{1}{3} - 2 x}{- 1 \frac{1}{2}} = - 3 \frac{1}{6}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{9 \frac{1}{3} - 2 x}{- 1 \frac{1}{2}}$ .

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Step 1.1.1

Convert $9 \frac{1}{3}$ to an improper fraction.

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Step 1.1.1.1

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

$\frac{9 + \frac{1}{3} - 2 x}{- 1 \frac{1}{2}} = - 3 \frac{1}{6}$

Step 1.1.1.2

Add $9$ and $\frac{1}{3}$ .

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Step 1.1.1.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9 \cdot \frac{3}{3} + \frac{1}{3} - 2 x}{- 1 \frac{1}{2}} = - 3 \frac{1}{6}$

Step 1.1.1.2.2

Combine $9$ and $\frac{3}{3}$ .

$\frac{\frac{9 \cdot 3}{3} + \frac{1}{3} - 2 x}{- 1 \frac{1}{2}} = - 3 \frac{1}{6}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{\frac{9 \cdot 3 + 1}{3} - 2 x}{- 1 \frac{1}{2}} = - 3 \frac{1}{6}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $9$ by $3$ .

$\frac{\frac{27 + 1}{3} - 2 x}{- 1 \frac{1}{2}} = - 3 \frac{1}{6}$

Step 1.1.1.2.4.2

Add $27$ and $1$ .

$\frac{\frac{28}{3} - 2 x}{- 1 \frac{1}{2}} = - 3 \frac{1}{6}$

Step 1.1.2

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

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Step 1.1.2.1

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

$\frac{\frac{28}{3} - 2 x}{- (1 + \frac{1}{2})} = - 3 \frac{1}{6}$

Step 1.1.2.2

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

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Step 1.1.2.2.1

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

$\frac{\frac{28}{3} - 2 x}{- (\frac{2}{2} + \frac{1}{2})} = - 3 \frac{1}{6}$

Step 1.1.2.2.2

Combine the numerators over the common denominator.

$\frac{\frac{28}{3} - 2 x}{- \frac{2 + 1}{2}} = - 3 \frac{1}{6}$

Step 1.1.2.2.3

Add $2$ and $1$ .

$\frac{\frac{28}{3} - 2 x}{- \frac{3}{2}} = - 3 \frac{1}{6}$

Step 1.1.3

Multiply the numerator by the reciprocal of the denominator.

$(\frac{28}{3} - 2 x) (- \frac{2}{3}) = - 3 \frac{1}{6}$

Step 1.1.4

Apply the distributive property.

$\frac{28}{3} (- \frac{2}{3}) - 2 x (- \frac{2}{3}) = - 3 \frac{1}{6}$

Step 1.1.5

Multiply $\frac{28}{3} (- \frac{2}{3})$ .

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Step 1.1.5.1

Multiply $\frac{28}{3}$ by $\frac{2}{3}$ .

$- \frac{28 \cdot 2}{3 \cdot 3} - 2 x (- \frac{2}{3}) = - 3 \frac{1}{6}$

Step 1.1.5.2

Multiply $28$ by $2$ .

$- \frac{56}{3 \cdot 3} - 2 x (- \frac{2}{3}) = - 3 \frac{1}{6}$

Step 1.1.5.3

Multiply $3$ by $3$ .

$- \frac{56}{9} - 2 x (- \frac{2}{3}) = - 3 \frac{1}{6}$

Step 1.1.6

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

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Step 1.1.6.1

Multiply $- 1$ by $- 2$ .

$- \frac{56}{9} + 2 x \frac{2}{3} = - 3 \frac{1}{6}$

Step 1.1.6.2

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

$- \frac{56}{9} + x \frac{2 \cdot 2}{3} = - 3 \frac{1}{6}$

Step 1.1.6.3

Multiply $2$ by $2$ .

$- \frac{56}{9} + x \frac{4}{3} = - 3 \frac{1}{6}$

Step 1.1.6.4

Combine $x$ and $\frac{4}{3}$ .

$- \frac{56}{9} + \frac{x \cdot 4}{3} = - 3 \frac{1}{6}$

Step 1.1.7

Move $4$ to the left of $x$ .

$- \frac{56}{9} + \frac{4 x}{3} = - 3 \frac{1}{6}$

Step 2

Simplify the right side.

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Step 2.1

Convert $3 \frac{1}{6}$ to an improper fraction.

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Step 2.1.1

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

$- \frac{56}{9} + \frac{4 x}{3} = - (3 + \frac{1}{6})$

Step 2.1.2

Add $3$ and $\frac{1}{6}$ .

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Step 2.1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- \frac{56}{9} + \frac{4 x}{3} = - (3 \cdot \frac{6}{6} + \frac{1}{6})$

Step 2.1.2.2

Combine $3$ and $\frac{6}{6}$ .

$- \frac{56}{9} + \frac{4 x}{3} = - (\frac{3 \cdot 6}{6} + \frac{1}{6})$

Step 2.1.2.3

Combine the numerators over the common denominator.

$- \frac{56}{9} + \frac{4 x}{3} = - \frac{3 \cdot 6 + 1}{6}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $3$ by $6$ .

$- \frac{56}{9} + \frac{4 x}{3} = - \frac{18 + 1}{6}$

Step 2.1.2.4.2

Add $18$ and $1$ .

$- \frac{56}{9} + \frac{4 x}{3} = - \frac{19}{6}$

Step 3

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

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Step 3.1

Add $\frac{56}{9}$ to both sides of the equation.

$\frac{4 x}{3} = - \frac{19}{6} + \frac{56}{9}$

Step 3.2

To write $- \frac{19}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4 x}{3} = - \frac{19}{6} \cdot \frac{3}{3} + \frac{56}{9}$

Step 3.3

To write $\frac{56}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 x}{3} = - \frac{19}{6} \cdot \frac{3}{3} + \frac{56}{9} \cdot \frac{2}{2}$

Step 3.4

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{19}{6}$ by $\frac{3}{3}$ .

$\frac{4 x}{3} = - \frac{19 \cdot 3}{6 \cdot 3} + \frac{56}{9} \cdot \frac{2}{2}$

Step 3.4.2

Multiply $6$ by $3$ .

$\frac{4 x}{3} = - \frac{19 \cdot 3}{18} + \frac{56}{9} \cdot \frac{2}{2}$

Step 3.4.3

Multiply $\frac{56}{9}$ by $\frac{2}{2}$ .

$\frac{4 x}{3} = - \frac{19 \cdot 3}{18} + \frac{56 \cdot 2}{9 \cdot 2}$

Step 3.4.4

Multiply $9$ by $2$ .

$\frac{4 x}{3} = - \frac{19 \cdot 3}{18} + \frac{56 \cdot 2}{18}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{4 x}{3} = \frac{- 19 \cdot 3 + 56 \cdot 2}{18}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $- 19$ by $3$ .

$\frac{4 x}{3} = \frac{- 57 + 56 \cdot 2}{18}$

Step 3.6.2

Multiply $56$ by $2$ .

$\frac{4 x}{3} = \frac{- 57 + 112}{18}$

Step 3.6.3

Add $- 57$ and $112$ .

$\frac{4 x}{3} = \frac{55}{18}$

Step 4

Multiply both sides of the equation by $\frac{3}{4}$ .

$\frac{3}{4} \cdot \frac{4 x}{3} = \frac{3}{4} \cdot \frac{55}{18}$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{3}{4} \cdot \frac{4 x}{3}$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{3}{4} \cdot \frac{4 x}{3} = \frac{3}{4} \cdot \frac{55}{18}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 x) = \frac{3}{4} \cdot \frac{55}{18}$

Step 5.1.1.2

Cancel the common factor of $4$ .

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Step 5.1.1.2.1

Factor $4$ out of $4 x$ .

$\frac{1}{4} (4 (x)) = \frac{3}{4} \cdot \frac{55}{18}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 x) = \frac{3}{4} \cdot \frac{55}{18}$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{3}{4} \cdot \frac{55}{18}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{3}{4} \cdot \frac{55}{18}$ .

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Step 5.2.1.1

Cancel the common factor of $3$ .

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Step 5.2.1.1.1

Factor $3$ out of $18$ .

$x = \frac{3}{4} \cdot \frac{55}{3 (6)}$

Step 5.2.1.1.2

Cancel the common factor.

$x = \frac{3}{4} \cdot \frac{55}{3 \cdot 6}$

Step 5.2.1.1.3

Rewrite the expression.

$x = \frac{1}{4} \cdot \frac{55}{6}$

Step 5.2.1.2

Multiply $\frac{1}{4}$ by $\frac{55}{6}$ .

$x = \frac{55}{4 \cdot 6}$

Step 5.2.1.3

Multiply $4$ by $6$ .

$x = \frac{55}{24}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{55}{24}$

Decimal Form:

$x = 2.291\overline{6}$

Mixed Number Form:

$x = 2 \frac{7}{24}$