Finite Math Examples

$8 x - 3 (- \frac{67}{63 z}) - 1 z = 0$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ .

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Step 1.1.1

Move the leading negative in $- \frac{67}{63 z}$ into the numerator.

$8 x - 3 \frac{- 67}{63 z} - 1 z = 0$

Step 1.1.2

Factor $3$ out of $- 3$ .

$8 x + 3 (- 1) \frac{- 67}{63 z} - 1 z = 0$

Step 1.1.3

Factor $3$ out of $63 z$ .

$8 x + 3 (- 1) \frac{- 67}{3 (21 z)} - 1 z = 0$

Step 1.1.4

Cancel the common factor.

$8 x + 3 \cdot - 1 \frac{- 67}{3 (21 z)} - 1 z = 0$

Step 1.1.5

Rewrite the expression.

$8 x - 1 \frac{- 67}{21 z} - 1 z = 0$

Step 1.2

Move the negative in front of the fraction.

$8 x - 1 (- \frac{67}{21 z}) - 1 z = 0$

Step 1.3

Multiply $- 1 (- \frac{67}{21 z})$ .

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Step 1.3.1

Multiply $- 1$ by $- 1$ .

$8 x + 1 \frac{67}{21 z} - 1 z = 0$

Step 1.3.2

Multiply $\frac{67}{21 z}$ by $1$ .

$8 x + \frac{67}{21 z} - 1 z = 0$

Step 1.4

Rewrite $- 1 z$ as $- z$ .

$8 x + \frac{67}{21 z} - z = 0$

Step 2

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

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Step 2.1

Subtract $\frac{67}{21 z}$ from both sides of the equation.

$8 x - z = - \frac{67}{21 z}$

Step 2.2

Add $z$ to both sides of the equation.

$8 x = - \frac{67}{21 z} + z$

Step 3

Divide each term in $8 x = - \frac{67}{21 z} + z$ by $8$ and simplify.

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Step 3.1

Divide each term in $8 x = - \frac{67}{21 z} + z$ by $8$ .

$\frac{8 x}{8} = \frac{- \frac{67}{21 z}}{8} + \frac{z}{8}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $8$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{- \frac{67}{21 z}}{8} + \frac{z}{8}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{67}{21 z}}{8} + \frac{z}{8}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{67}{21 z} \cdot \frac{1}{8} + \frac{z}{8}$

Step 3.3.1.2

Multiply $- \frac{67}{21 z} \cdot \frac{1}{8}$ .

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Step 3.3.1.2.1

Multiply $\frac{1}{8}$ by $\frac{67}{21 z}$ .

$x = - \frac{67}{8 (21 z)} + \frac{z}{8}$

Step 3.3.1.2.2

Multiply $21$ by $8$ .

$x = - \frac{67}{168 z} + \frac{z}{8}$