Calculus Examples

$\frac{56}{3} - \frac{8 x}{9} = 0$

Step 1

Subtract $\frac{56}{3}$ from both sides of the equation.

$- \frac{8 x}{9} = - \frac{56}{3}$

Step 2

Multiply both sides of the equation by $- \frac{9}{8}$ .

$- \frac{9}{8} (- \frac{8 x}{9}) = - \frac{9}{8} (- \frac{56}{3})$

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 $- \frac{9}{8} (- \frac{8 x}{9})$ .

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Step 3.1.1.1

Cancel the common factor of $9$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{9}{8}$ into the numerator.

$\frac{- 9}{8} (- \frac{8 x}{9}) = - \frac{9}{8} (- \frac{56}{3})$

Step 3.1.1.1.2

Move the leading negative in $- \frac{8 x}{9}$ into the numerator.

$\frac{- 9}{8} \cdot \frac{- 8 x}{9} = - \frac{9}{8} (- \frac{56}{3})$

Step 3.1.1.1.3

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{8} \cdot \frac{- 8 x}{9} = - \frac{9}{8} (- \frac{56}{3})$

Step 3.1.1.1.4

Cancel the common factor.

$\frac{9 \cdot - 1}{8} \cdot \frac{- 8 x}{9} = - \frac{9}{8} (- \frac{56}{3})$

Step 3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{8} (- 8 x) = - \frac{9}{8} (- \frac{56}{3})$

Step 3.1.1.2

Cancel the common factor of $8$ .

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Step 3.1.1.2.1

Factor $8$ out of $- 8 x$ .

$\frac{- 1}{8} (8 (- x)) = - \frac{9}{8} (- \frac{56}{3})$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{8} (8 (- x)) = - \frac{9}{8} (- \frac{56}{3})$

Step 3.1.1.2.3

Rewrite the expression.

$- - x = - \frac{9}{8} (- \frac{56}{3})$

Step 3.1.1.3

Multiply.

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Step 3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{9}{8} (- \frac{56}{3})$

Step 3.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{9}{8} (- \frac{56}{3})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{9}{8} (- \frac{56}{3})$ .

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Step 3.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{9}{8}$ into the numerator.

$x = \frac{- 9}{8} (- \frac{56}{3})$

Step 3.2.1.1.2

Move the leading negative in $- \frac{56}{3}$ into the numerator.

$x = \frac{- 9}{8} \cdot \frac{- 56}{3}$

Step 3.2.1.1.3

Factor $3$ out of $- 9$ .

$x = \frac{3 (- 3)}{8} \cdot \frac{- 56}{3}$

Step 3.2.1.1.4

Cancel the common factor.

$x = \frac{3 \cdot - 3}{8} \cdot \frac{- 56}{3}$

Step 3.2.1.1.5

Rewrite the expression.

$x = \frac{- 3}{8} \cdot - 56$

Step 3.2.1.2

Cancel the common factor of $8$ .

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Step 3.2.1.2.1

Factor $8$ out of $- 56$ .

$x = \frac{- 3}{8} \cdot (8 (- 7))$

Step 3.2.1.2.2

Cancel the common factor.

$x = \frac{- 3}{8} \cdot (8 \cdot - 7)$

Step 3.2.1.2.3

Rewrite the expression.

$x = - 3 \cdot - 7$

Step 3.2.1.3

Multiply $- 3$ by $- 7$ .

$x = 21$