Finite Math Examples

$\frac{7}{10} z - 4 z + \frac{1}{5} = \frac{2}{5}$

Step 1

Simplify $\frac{7}{10} z - 4 z + \frac{1}{5}$ .

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Step 1.1

Combine $\frac{7}{10}$ and $z$ .

$\frac{7 z}{10} - 4 z + \frac{1}{5} = \frac{2}{5}$

Step 1.2

To write $- 4 z$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{7 z}{10} - 4 z \cdot \frac{10}{10} + \frac{1}{5} = \frac{2}{5}$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $- 4 z$ and $\frac{10}{10}$ .

$\frac{7 z}{10} + \frac{- 4 z \cdot 10}{10} + \frac{1}{5} = \frac{2}{5}$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{7 z - 4 z \cdot 10}{10} + \frac{1}{5} = \frac{2}{5}$

Step 1.4

Simplify each term.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Factor $z$ out of $7 z - 4 z \cdot 10$ .

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Step 1.4.1.1.1

Factor $z$ out of $7 z$ .

$\frac{z \cdot 7 - 4 z \cdot 10}{10} + \frac{1}{5} = \frac{2}{5}$

Step 1.4.1.1.2

Factor $z$ out of $- 4 z \cdot 10$ .

$\frac{z \cdot 7 + z (- 4 \cdot 10)}{10} + \frac{1}{5} = \frac{2}{5}$

Step 1.4.1.1.3

Factor $z$ out of $z \cdot 7 + z (- 4 \cdot 10)$ .

$\frac{z (7 - 4 \cdot 10)}{10} + \frac{1}{5} = \frac{2}{5}$

Step 1.4.1.2

Multiply $- 4$ by $10$ .

$\frac{z (7 - 40)}{10} + \frac{1}{5} = \frac{2}{5}$

Step 1.4.1.3

Subtract $40$ from $7$ .

$\frac{z \cdot - 33}{10} + \frac{1}{5} = \frac{2}{5}$

Step 1.4.2

Move $- 33$ to the left of $z$ .

$\frac{- 33 \cdot z}{10} + \frac{1}{5} = \frac{2}{5}$

Step 1.4.3

Move the negative in front of the fraction.

$- \frac{33 z}{10} + \frac{1}{5} = \frac{2}{5}$

Step 2

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

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Step 2.1

Subtract $\frac{1}{5}$ from both sides of the equation.

$- \frac{33 z}{10} = \frac{2}{5} - \frac{1}{5}$

Step 2.2

Combine the numerators over the common denominator.

$- \frac{33 z}{10} = \frac{2 - 1}{5}$

Step 2.3

Subtract $1$ from $2$ .

$- \frac{33 z}{10} = \frac{1}{5}$

Step 3

Multiply both sides of the equation by $- \frac{10}{33}$ .

$- \frac{10}{33} (- \frac{33 z}{10}) = - \frac{10}{33} \cdot \frac{1}{5}$

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 $- \frac{10}{33} (- \frac{33 z}{10})$ .

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Step 4.1.1.1

Cancel the common factor of $10$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{10}{33}$ into the numerator.

$\frac{- 10}{33} (- \frac{33 z}{10}) = - \frac{10}{33} \cdot \frac{1}{5}$

Step 4.1.1.1.2

Move the leading negative in $- \frac{33 z}{10}$ into the numerator.

$\frac{- 10}{33} \cdot \frac{- 33 z}{10} = - \frac{10}{33} \cdot \frac{1}{5}$

Step 4.1.1.1.3

Factor $10$ out of $- 10$ .

$\frac{10 (- 1)}{33} \cdot \frac{- 33 z}{10} = - \frac{10}{33} \cdot \frac{1}{5}$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{10 \cdot - 1}{33} \cdot \frac{- 33 z}{10} = - \frac{10}{33} \cdot \frac{1}{5}$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{33} (- 33 z) = - \frac{10}{33} \cdot \frac{1}{5}$

Step 4.1.1.2

Cancel the common factor of $33$ .

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Step 4.1.1.2.1

Factor $33$ out of $- 33 z$ .

$\frac{- 1}{33} (33 (- z)) = - \frac{10}{33} \cdot \frac{1}{5}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{33} (33 (- z)) = - \frac{10}{33} \cdot \frac{1}{5}$

Step 4.1.1.2.3

Rewrite the expression.

$- - z = - \frac{10}{33} \cdot \frac{1}{5}$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 z = - \frac{10}{33} \cdot \frac{1}{5}$

Step 4.1.1.3.2

Multiply $z$ by $1$ .

$z = - \frac{10}{33} \cdot \frac{1}{5}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{10}{33} \cdot \frac{1}{5}$ .

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Step 4.2.1.1

Cancel the common factor of $5$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{10}{33}$ into the numerator.

$z = \frac{- 10}{33} \cdot \frac{1}{5}$

Step 4.2.1.1.2

Factor $5$ out of $- 10$ .

$z = \frac{5 (- 2)}{33} \cdot \frac{1}{5}$

Step 4.2.1.1.3

Cancel the common factor.

$z = \frac{5 \cdot - 2}{33} \cdot \frac{1}{5}$

Step 4.2.1.1.4

Rewrite the expression.

$z = \frac{- 2}{33}$

Step 4.2.1.2

Move the negative in front of the fraction.

$z = - \frac{2}{33}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{2}{33}$

Decimal Form:

$z = - 0.\overline{06}$