Pre-Algebra Examples

$- \frac{3}{5} z - 4 = - \frac{77}{20}$

Step 1

Simplify each term.

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Step 1.1

Combine $z$ and $\frac{3}{5}$ .

$- \frac{z \cdot 3}{5} - 4 = - \frac{77}{20}$

Step 1.2

Move $3$ to the left of $z$ .

$- \frac{3 z}{5} - 4 = - \frac{77}{20}$

Step 2

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

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Step 2.1

Add $4$ to both sides of the equation.

$- \frac{3 z}{5} = - \frac{77}{20} + 4$

Step 2.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$- \frac{3 z}{5} = - \frac{77}{20} + 4 \cdot \frac{20}{20}$

Step 2.3

Combine $4$ and $\frac{20}{20}$ .

$- \frac{3 z}{5} = - \frac{77}{20} + \frac{4 \cdot 20}{20}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{3 z}{5} = \frac{- 77 + 4 \cdot 20}{20}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $4$ by $20$ .

$- \frac{3 z}{5} = \frac{- 77 + 80}{20}$

Step 2.5.2

Add $- 77$ and $80$ .

$- \frac{3 z}{5} = \frac{3}{20}$

Step 3

Multiply both sides of the equation by $- \frac{5}{3}$ .

$- \frac{5}{3} (- \frac{3 z}{5}) = - \frac{5}{3} \cdot \frac{3}{20}$

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 $- \frac{5}{3} (- \frac{3 z}{5})$ .

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$\frac{- 5}{3} (- \frac{3 z}{5}) = - \frac{5}{3} \cdot \frac{3}{20}$

Step 4.1.1.1.2

Move the leading negative in $- \frac{3 z}{5}$ into the numerator.

$\frac{- 5}{3} \cdot \frac{- 3 z}{5} = - \frac{5}{3} \cdot \frac{3}{20}$

Step 4.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{3} \cdot \frac{- 3 z}{5} = - \frac{5}{3} \cdot \frac{3}{20}$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{3} \cdot \frac{- 3 z}{5} = - \frac{5}{3} \cdot \frac{3}{20}$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 z) = - \frac{5}{3} \cdot \frac{3}{20}$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Factor $3$ out of $- 3 z$ .

$\frac{- 1}{3} (3 (- z)) = - \frac{5}{3} \cdot \frac{3}{20}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- z)) = - \frac{5}{3} \cdot \frac{3}{20}$

Step 4.1.1.2.3

Rewrite the expression.

$- - z = - \frac{5}{3} \cdot \frac{3}{20}$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 z = - \frac{5}{3} \cdot \frac{3}{20}$

Step 4.1.1.3.2

Multiply $z$ by $1$ .

$z = - \frac{5}{3} \cdot \frac{3}{20}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{5}{3} \cdot \frac{3}{20}$ .

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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 $- \frac{5}{3}$ into the numerator.

$z = \frac{- 5}{3} \cdot \frac{3}{20}$

Step 4.2.1.1.2

Factor $5$ out of $- 5$ .

$z = \frac{5 (- 1)}{3} \cdot \frac{3}{20}$

Step 4.2.1.1.3

Factor $5$ out of $20$ .

$z = \frac{5 \cdot - 1}{3} \cdot \frac{3}{5 \cdot 4}$

Step 4.2.1.1.4

Cancel the common factor.

$z = \frac{5 \cdot - 1}{3} \cdot \frac{3}{5 \cdot 4}$

Step 4.2.1.1.5

Rewrite the expression.

$z = \frac{- 1}{3} \cdot \frac{3}{4}$

Step 4.2.1.2

Cancel the common factor of $3$ .

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Step 4.2.1.2.1

Cancel the common factor.

$z = \frac{- 1}{3} \cdot \frac{3}{4}$

Step 4.2.1.2.2

Rewrite the expression.

$z = - \frac{1}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{1}{4}$

Decimal Form:

$z = - 0.25$