Calculus Examples

$x = \frac{11}{3} \cdot ((\frac{1}{3}) x) + \frac{7}{3}$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{11}{3} \cdot \frac{1}{3}$ .

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Step 1.1.1

Multiply $\frac{11}{3}$ by $\frac{1}{3}$ .

$x = \frac{11}{3 \cdot 3} \cdot x + \frac{7}{3}$

Step 1.1.2

Multiply $3$ by $3$ .

$x = \frac{11}{9} \cdot x + \frac{7}{3}$

Step 1.2

Combine $\frac{11}{9}$ and $x$ .

$x = \frac{11 x}{9} + \frac{7}{3}$

Step 2

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

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Step 2.1

Subtract $\frac{11 x}{9}$ from both sides of the equation.

$x - \frac{11 x}{9} = \frac{7}{3}$

Step 2.2

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

$x \cdot \frac{9}{9} - \frac{11 x}{9} = \frac{7}{3}$

Step 2.3

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

$\frac{x \cdot 9}{9} - \frac{11 x}{9} = \frac{7}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{x \cdot 9 - 11 x}{9} = \frac{7}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Move $9$ to the left of $x$ .

$\frac{9 \cdot x - 11 x}{9} = \frac{7}{3}$

Step 2.5.2

Subtract $11 x$ from $9 x$ .

$\frac{- 2 x}{9} = \frac{7}{3}$

Step 2.6

Move the negative in front of the fraction.

$- \frac{2 x}{9} = \frac{7}{3}$

Step 3

Multiply both sides of the equation by $- \frac{9}{2}$ .

$- \frac{9}{2} (- \frac{2 x}{9}) = - \frac{9}{2} \cdot \frac{7}{3}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- \frac{9}{2} (- \frac{2 x}{9})$ .

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Step 4.1.1.1

Cancel the common factor of $9$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$\frac{- 9}{2} (- \frac{2 x}{9}) = - \frac{9}{2} \cdot \frac{7}{3}$

Step 4.1.1.1.2

Move the leading negative in $- \frac{2 x}{9}$ into the numerator.

$\frac{- 9}{2} \cdot \frac{- 2 x}{9} = - \frac{9}{2} \cdot \frac{7}{3}$

Step 4.1.1.1.3

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{2} \cdot \frac{- 2 x}{9} = - \frac{9}{2} \cdot \frac{7}{3}$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{9 \cdot - 1}{2} \cdot \frac{- 2 x}{9} = - \frac{9}{2} \cdot \frac{7}{3}$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} (- 2 x) = - \frac{9}{2} \cdot \frac{7}{3}$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Factor $2$ out of $- 2 x$ .

$\frac{- 1}{2} (2 (- x)) = - \frac{9}{2} \cdot \frac{7}{3}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} (2 (- x)) = - \frac{9}{2} \cdot \frac{7}{3}$

Step 4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{9}{2} \cdot \frac{7}{3}$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{9}{2} \cdot \frac{7}{3}$

Step 4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{9}{2} \cdot \frac{7}{3}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{9}{2} \cdot \frac{7}{3}$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$x = \frac{- 9}{2} \cdot \frac{7}{3}$

Step 4.2.1.1.2

Factor $3$ out of $- 9$ .

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

Step 4.2.1.1.3

Cancel the common factor.

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

Step 4.2.1.1.4

Rewrite the expression.

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

Step 4.2.1.2

Combine $\frac{- 3}{2}$ and $7$ .

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

Step 4.2.1.3

Simplify the expression.

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Step 4.2.1.3.1

Multiply $- 3$ by $7$ .

$x = \frac{- 21}{2}$

Step 4.2.1.3.2

Move the negative in front of the fraction.

$x = - \frac{21}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{21}{2}$

Decimal Form:

$x = - 10.5$

Mixed Number Form:

$x = - 10 \frac{1}{2}$