Algebra Examples

$\frac{635}{72} = - \frac{5}{2} (- \frac{11}{4} + x)$

Step 1

Rewrite the equation as $- \frac{5}{2} \cdot (- \frac{11}{4} + x) = \frac{635}{72}$ .

$- \frac{5}{2} \cdot (- \frac{11}{4} + x) = \frac{635}{72}$

Step 2

Multiply both sides of the equation by $- \frac{2}{5}$ .

$- \frac{2}{5} (- \frac{5}{2} \cdot (- \frac{11}{4} + x)) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- \frac{2}{5} (- \frac{5}{2} \cdot (- \frac{11}{4} + x))$ .

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Step 3.1.1.1

Apply the distributive property.

$- \frac{2}{5} (- \frac{5}{2} (- \frac{11}{4}) - \frac{5}{2} x) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.2

Multiply $- \frac{5}{2} (- \frac{11}{4})$ .

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$- \frac{2}{5} (1 (\frac{5}{2}) \frac{11}{4} - \frac{5}{2} x) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.2.2

Multiply $\frac{5}{2}$ by $1$ .

$- \frac{2}{5} (\frac{5}{2} \cdot \frac{11}{4} - \frac{5}{2} x) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.2.3

Multiply $\frac{5}{2}$ by $\frac{11}{4}$ .

$- \frac{2}{5} (\frac{5 \cdot 11}{2 \cdot 4} - \frac{5}{2} x) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.2.4

Multiply $5$ by $11$ .

$- \frac{2}{5} (\frac{55}{2 \cdot 4} - \frac{5}{2} x) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.2.5

Multiply $2$ by $4$ .

$- \frac{2}{5} (\frac{55}{8} - \frac{5}{2} x) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.3

Combine $x$ and $\frac{5}{2}$ .

$- \frac{2}{5} (\frac{55}{8} - \frac{x \cdot 5}{2}) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.4

Move $5$ to the left of $x$ .

$- \frac{2}{5} (\frac{55}{8} - \frac{5 x}{2}) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5

Simplify terms.

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Step 3.1.1.5.1

Apply the distributive property.

$- \frac{2}{5} \cdot \frac{55}{8} - \frac{2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.2

Cancel the common factor of $2$ .

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Step 3.1.1.5.2.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{- 2}{5} \cdot \frac{55}{8} - \frac{2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.2.2

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{5} \cdot \frac{55}{8} - \frac{2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.2.3

Factor $2$ out of $8$ .

$\frac{2 \cdot - 1}{5} \cdot \frac{55}{2 \cdot 4} - \frac{2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.2.4

Cancel the common factor.

$\frac{2 \cdot - 1}{5} \cdot \frac{55}{2 \cdot 4} - \frac{2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.2.5

Rewrite the expression.

$\frac{- 1}{5} \cdot \frac{55}{4} - \frac{2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.3

Cancel the common factor of $5$ .

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Step 3.1.1.5.3.1

Factor $5$ out of $55$ .

$\frac{- 1}{5} \cdot \frac{5 (11)}{4} - \frac{2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.3.2

Cancel the common factor.

$\frac{- 1}{5} \cdot \frac{5 \cdot 11}{4} - \frac{2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.3.3

Rewrite the expression.

$- \frac{11}{4} - \frac{2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.4

Cancel the common factor of $2$ .

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Step 3.1.1.5.4.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$- \frac{11}{4} + \frac{- 2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.4.2

Move the leading negative in $- \frac{5 x}{2}$ into the numerator.

$- \frac{11}{4} + \frac{- 2}{5} \cdot \frac{- 5 x}{2} = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.4.3

Factor $2$ out of $- 2$ .

$- \frac{11}{4} + \frac{2 (- 1)}{5} \cdot \frac{- 5 x}{2} = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.4.4

Cancel the common factor.

$- \frac{11}{4} + \frac{2 \cdot - 1}{5} \cdot \frac{- 5 x}{2} = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.4.5

Rewrite the expression.

$- \frac{11}{4} + \frac{- 1}{5} (- 5 x) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.5

Cancel the common factor of $5$ .

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Step 3.1.1.5.5.1

Factor $5$ out of $- 5 x$ .

$- \frac{11}{4} + \frac{- 1}{5} (5 (- x)) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.5.2

Cancel the common factor.

$- \frac{11}{4} + \frac{- 1}{5} (5 (- x)) = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.5.3

Rewrite the expression.

$- \frac{11}{4} - - x = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.6

Multiply.

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Step 3.1.1.5.6.1

Multiply $- 1$ by $- 1$ .

$- \frac{11}{4} + 1 x = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.1.1.5.6.2

Multiply $x$ by $1$ .

$- \frac{11}{4} + x = - \frac{2}{5} \cdot \frac{635}{72}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{2}{5} \cdot \frac{635}{72}$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$- \frac{11}{4} + x = \frac{- 2}{5} \cdot \frac{635}{72}$

Step 3.2.1.1.2

Factor $2$ out of $- 2$ .

$- \frac{11}{4} + x = \frac{2 (- 1)}{5} \cdot \frac{635}{72}$

Step 3.2.1.1.3

Factor $2$ out of $72$ .

$- \frac{11}{4} + x = \frac{2 \cdot - 1}{5} \cdot \frac{635}{2 \cdot 36}$

Step 3.2.1.1.4

Cancel the common factor.

$- \frac{11}{4} + x = \frac{2 \cdot - 1}{5} \cdot \frac{635}{2 \cdot 36}$

Step 3.2.1.1.5

Rewrite the expression.

$- \frac{11}{4} + x = \frac{- 1}{5} \cdot \frac{635}{36}$

Step 3.2.1.2

Cancel the common factor of $5$ .

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Step 3.2.1.2.1

Factor $5$ out of $635$ .

$- \frac{11}{4} + x = \frac{- 1}{5} \cdot \frac{5 (127)}{36}$

Step 3.2.1.2.2

Cancel the common factor.

$- \frac{11}{4} + x = \frac{- 1}{5} \cdot \frac{5 \cdot 127}{36}$

Step 3.2.1.2.3

Rewrite the expression.

$- \frac{11}{4} + x = - \frac{127}{36}$

Step 4

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

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Step 4.1

Add $\frac{11}{4}$ to both sides of the equation.

$x = - \frac{127}{36} + \frac{11}{4}$

Step 4.2

To write $\frac{11}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$x = - \frac{127}{36} + \frac{11}{4} \cdot \frac{9}{9}$

Step 4.3

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.1

Multiply $\frac{11}{4}$ by $\frac{9}{9}$ .

$x = - \frac{127}{36} + \frac{11 \cdot 9}{4 \cdot 9}$

Step 4.3.2

Multiply $4$ by $9$ .

$x = - \frac{127}{36} + \frac{11 \cdot 9}{36}$

Step 4.4

Combine the numerators over the common denominator.

$x = \frac{- 127 + 11 \cdot 9}{36}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $11$ by $9$ .

$x = \frac{- 127 + 99}{36}$

Step 4.5.2

Add $- 127$ and $99$ .

$x = \frac{- 28}{36}$

Step 4.6

Cancel the common factor of $- 28$ and $36$ .

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Step 4.6.1

Factor $4$ out of $- 28$ .

$x = \frac{4 (- 7)}{36}$

Step 4.6.2

Cancel the common factors.

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Step 4.6.2.1

Factor $4$ out of $36$ .

$x = \frac{4 \cdot - 7}{4 \cdot 9}$

Step 4.6.2.2

Cancel the common factor.

$x = \frac{4 \cdot - 7}{4 \cdot 9}$

Step 4.6.2.3

Rewrite the expression.

$x = \frac{- 7}{9}$

Step 4.7

Move the negative in front of the fraction.

$x = - \frac{7}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7}{9}$

Decimal Form:

$x = - 0.\overline{7}$