Algebra Examples

$3 \frac{1}{8} \div (x - 4 \frac{7}{28}) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $3 \frac{1}{8} \div (x - 4 \frac{7}{28})$ .

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Step 1.1.1

Convert $3 \frac{1}{8}$ 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.

$(3 + \frac{1}{8}) \div (x - 4 \frac{7}{28}) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.1.2

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

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Step 1.1.1.2.1

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

$(3 \cdot \frac{8}{8} + \frac{1}{8}) \div (x - 4 \frac{7}{28}) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.1.2.2

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

$(\frac{3 \cdot 8}{8} + \frac{1}{8}) \div (x - 4 \frac{7}{28}) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 8 + 1}{8} \div (x - 4 \frac{7}{28}) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $3$ by $8$ .

$\frac{24 + 1}{8} \div (x - 4 \frac{7}{28}) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.1.2.4.2

Add $24$ and $1$ .

$\frac{25}{8} \div (x - 4 \frac{7}{28}) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.2

Convert $4 \frac{7}{28}$ 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.

$\frac{25}{8} \div (x - (4 + \frac{7}{28})) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.2.2

Add $4$ and $\frac{7}{28}$ .

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Step 1.1.2.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{28}{28}$ .

$\frac{25}{8} \div (x - (4 \cdot \frac{28}{28} + \frac{7}{28})) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.2.2.2

Combine $4$ and $\frac{28}{28}$ .

$\frac{25}{8} \div (x - (\frac{4 \cdot 28}{28} + \frac{7}{28})) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{25}{8} \div (x - \frac{4 \cdot 28 + 7}{28}) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $4$ by $28$ .

$\frac{25}{8} \div (x - \frac{112 + 7}{28}) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.2.2.4.2

Add $112$ and $7$ .

$\frac{25}{8} \div (x - \frac{119}{28}) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.3

Rewrite the division as a fraction.

$\frac{\frac{25}{8}}{x - \frac{119}{28}} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.4

Cancel the common factor of $119$ and $28$ .

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Step 1.1.4.1

Factor $7$ out of $119$ .

$\frac{\frac{25}{8}}{x - \frac{7 (17)}{28}} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.4.2

Cancel the common factors.

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Step 1.1.4.2.1

Factor $7$ out of $28$ .

$\frac{\frac{25}{8}}{x - \frac{7 \cdot 17}{7 \cdot 4}} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.4.2.2

Cancel the common factor.

$\frac{\frac{25}{8}}{x - \frac{7 \cdot 17}{7 \cdot 4}} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.4.2.3

Rewrite the expression.

$\frac{\frac{25}{8}}{x - \frac{17}{4}} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.5

Multiply the numerator by the reciprocal of the denominator.

$\frac{25}{8} \cdot \frac{1}{x - \frac{17}{4}} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.6

Simplify the denominator.

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Step 1.1.6.1

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

$\frac{25}{8} \cdot \frac{1}{x \cdot \frac{4}{4} - \frac{17}{4}} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.6.2

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

$\frac{25}{8} \cdot \frac{1}{\frac{x \cdot 4}{4} - \frac{17}{4}} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.6.3

Combine the numerators over the common denominator.

$\frac{25}{8} \cdot \frac{1}{\frac{x \cdot 4 - 17}{4}} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.6.4

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

$\frac{25}{8} \cdot \frac{1}{\frac{4 x - 17}{4}} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.7

Multiply the numerator by the reciprocal of the denominator.

$\frac{25}{8} (1 \frac{4}{4 x - 17}) = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.8

Multiply $\frac{4}{4 x - 17}$ by $1$ .

$\frac{25}{8} \cdot \frac{4}{4 x - 17} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.9

Cancel the common factor of $4$ .

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Step 1.1.9.1

Factor $4$ out of $8$ .

$\frac{25}{4 (2)} \cdot \frac{4}{4 x - 17} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.9.2

Cancel the common factor.

$\frac{25}{4 \cdot 2} \cdot \frac{4}{4 x - 17} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.9.3

Rewrite the expression.

$\frac{25}{2} \cdot \frac{1}{4 x - 17} = \frac{17}{18} + 1 \frac{5}{6}$

Step 1.1.10

Multiply $\frac{25}{2}$ by $\frac{1}{4 x - 17}$ .

$\frac{25}{2 (4 x - 17)} = \frac{17}{18} + 1 \frac{5}{6}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $\frac{17}{18} + 1 \frac{5}{6}$ .

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Step 2.1.1

Convert $1 \frac{5}{6}$ 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.

$\frac{25}{2 (4 x - 17)} = \frac{17}{18} + 1 + \frac{5}{6}$

Step 2.1.1.2

Add $1$ and $\frac{5}{6}$ .

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Step 2.1.1.2.1

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

$\frac{25}{2 (4 x - 17)} = \frac{17}{18} + \frac{6}{6} + \frac{5}{6}$

Step 2.1.1.2.2

Combine the numerators over the common denominator.

$\frac{25}{2 (4 x - 17)} = \frac{17}{18} + \frac{6 + 5}{6}$

Step 2.1.1.2.3

Add $6$ and $5$ .

$\frac{25}{2 (4 x - 17)} = \frac{17}{18} + \frac{11}{6}$

Step 2.1.2

To write $\frac{11}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{25}{2 (4 x - 17)} = \frac{17}{18} + \frac{11}{6} \cdot \frac{3}{3}$

Step 2.1.3

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

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Step 2.1.3.1

Multiply $\frac{11}{6}$ by $\frac{3}{3}$ .

$\frac{25}{2 (4 x - 17)} = \frac{17}{18} + \frac{11 \cdot 3}{6 \cdot 3}$

Step 2.1.3.2

Multiply $6$ by $3$ .

$\frac{25}{2 (4 x - 17)} = \frac{17}{18} + \frac{11 \cdot 3}{18}$

Step 2.1.4

Combine the numerators over the common denominator.

$\frac{25}{2 (4 x - 17)} = \frac{17 + 11 \cdot 3}{18}$

Step 2.1.5

Simplify the numerator.

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Step 2.1.5.1

Multiply $11$ by $3$ .

$\frac{25}{2 (4 x - 17)} = \frac{17 + 33}{18}$

Step 2.1.5.2

Add $17$ and $33$ .

$\frac{25}{2 (4 x - 17)} = \frac{50}{18}$

Step 2.1.6

Cancel the common factor of $50$ and $18$ .

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Step 2.1.6.1

Factor $2$ out of $50$ .

$\frac{25}{2 (4 x - 17)} = \frac{2 (25)}{18}$

Step 2.1.6.2

Cancel the common factors.

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Step 2.1.6.2.1

Factor $2$ out of $18$ .

$\frac{25}{2 (4 x - 17)} = \frac{2 \cdot 25}{2 \cdot 9}$

Step 2.1.6.2.2

Cancel the common factor.

$\frac{25}{2 (4 x - 17)} = \frac{2 \cdot 25}{2 \cdot 9}$

Step 2.1.6.2.3

Rewrite the expression.

$\frac{25}{2 (4 x - 17)} = \frac{25}{9}$

Step 3

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$25 \cdot 9 = 2 (4 x - 17) \cdot 25$

Step 4

Solve the equation for $x$ .

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Step 4.1

Rewrite the equation as $2 (4 x - 17) \cdot 25 = 25 \cdot 9$ .

$2 (4 x - 17) \cdot 25 = 25 \cdot 9$

Step 4.2

Simplify.

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Step 4.2.1

Multiply $25$ by $2$ .

$50 (4 x - 17) = 25 \cdot 9$

Step 4.2.2

Multiply $25$ by $9$ .

$50 (4 x - 17) = 225$

Step 4.3

Divide each term in $50 (4 x - 17) = 225$ by $50$ and simplify.

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Step 4.3.1

Divide each term in $50 (4 x - 17) = 225$ by $50$ .

$\frac{50 (4 x - 17)}{50} = \frac{225}{50}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $50$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{50 (4 x - 17)}{50} = \frac{225}{50}$

Step 4.3.2.1.2

Divide $4 x - 17$ by $1$ .

$4 x - 17 = \frac{225}{50}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $225$ and $50$ .

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Step 4.3.3.1.1

Factor $25$ out of $225$ .

$4 x - 17 = \frac{25 (9)}{50}$

Step 4.3.3.1.2

Cancel the common factors.

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Step 4.3.3.1.2.1

Factor $25$ out of $50$ .

$4 x - 17 = \frac{25 \cdot 9}{25 \cdot 2}$

Step 4.3.3.1.2.2

Cancel the common factor.

$4 x - 17 = \frac{25 \cdot 9}{25 \cdot 2}$

Step 4.3.3.1.2.3

Rewrite the expression.

$4 x - 17 = \frac{9}{2}$

Step 4.4

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

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Step 4.4.1

Add $17$ to both sides of the equation.

$4 x = \frac{9}{2} + 17$

Step 4.4.2

To write $17$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 x = \frac{9}{2} + 17 \cdot \frac{2}{2}$

Step 4.4.3

Combine $17$ and $\frac{2}{2}$ .

$4 x = \frac{9}{2} + \frac{17 \cdot 2}{2}$

Step 4.4.4

Combine the numerators over the common denominator.

$4 x = \frac{9 + 17 \cdot 2}{2}$

Step 4.4.5

Simplify the numerator.

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Step 4.4.5.1

Multiply $17$ by $2$ .

$4 x = \frac{9 + 34}{2}$

Step 4.4.5.2

Add $9$ and $34$ .

$4 x = \frac{43}{2}$

Step 4.5

Divide each term in $4 x = \frac{43}{2}$ by $4$ and simplify.

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Step 4.5.1

Divide each term in $4 x = \frac{43}{2}$ by $4$ .

$\frac{4 x}{4} = \frac{\frac{43}{2}}{4}$

Step 4.5.2

Simplify the left side.

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Step 4.5.2.1

Cancel the common factor of $4$ .

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Step 4.5.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{\frac{43}{2}}{4}$

Step 4.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{43}{2}}{4}$

Step 4.5.3

Simplify the right side.

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Step 4.5.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{43}{2} \cdot \frac{1}{4}$

Step 4.5.3.2

Multiply $\frac{43}{2} \cdot \frac{1}{4}$ .

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Step 4.5.3.2.1

Multiply $\frac{43}{2}$ by $\frac{1}{4}$ .

$x = \frac{43}{2 \cdot 4}$

Step 4.5.3.2.2

Multiply $2$ by $4$ .

$x = \frac{43}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{43}{8}$

Decimal Form:

$x = 5.375$

Mixed Number Form:

$x = 5 \frac{3}{8}$