Finite Math Examples

$z = \frac{48 - 40 x}{8}$

Step 1

Rewrite the equation as $\frac{48 - 40 x}{8} = z$ .

$\frac{48 - 40 x}{8} = z$

Step 2

Cancel the common factor of $48 - 40 x$ and $8$ .

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Step 2.1

Factor $8$ out of $48$ .

$\frac{8 \cdot 6 - 40 x}{8} = z$

Step 2.2

Factor $8$ out of $- 40 x$ .

$\frac{8 \cdot 6 + 8 (- 5 x)}{8} = z$

Step 2.3

Factor $8$ out of $8 (6) + 8 (- 5 x)$ .

$\frac{8 (6 - 5 x)}{8} = z$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $8$ out of $8$ .

$\frac{8 (6 - 5 x)}{8 (1)} = z$

Step 2.4.2

Cancel the common factor.

$\frac{8 (6 - 5 x)}{8 \cdot 1} = z$

Step 2.4.3

Rewrite the expression.

$\frac{6 - 5 x}{1} = z$

Step 2.4.4

Divide $6 - 5 x$ by $1$ .

$6 - 5 x = z$

Step 3

Solve for $x$ .

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Step 3.1

Subtract $6$ from both sides of the equation.

$- 5 x = z - 6$

Step 3.2

Divide each term in $- 5 x = z - 6$ by $- 5$ and simplify.

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Step 3.2.1

Divide each term in $- 5 x = z - 6$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{z}{- 5} + \frac{- 6}{- 5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{z}{- 5} + \frac{- 6}{- 5}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{z}{- 5} + \frac{- 6}{- 5}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

Move the negative in front of the fraction.

$x = - \frac{z}{5} + \frac{- 6}{- 5}$

Step 3.2.3.1.2

Dividing two negative values results in a positive value.

$x = - \frac{z}{5} + \frac{6}{5}$