Basic Math Examples

$4 - \frac{3}{5} z = 13$

Step 1

Simplify each term.

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Step 1.1

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

$4 - \frac{z \cdot 3}{5} = 13$

Step 1.2

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

$4 - \frac{3 z}{5} = 13$

Step 2

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

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Step 2.1

Subtract $4$ from both sides of the equation.

$- \frac{3 z}{5} = 13 - 4$

Step 2.2

Subtract $4$ from $13$ .

$- \frac{3 z}{5} = 9$

Step 3

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

$- \frac{5}{3} (- \frac{3 z}{5}) = - \frac{5}{3} \cdot 9$

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.

$\frac{- 5}{3} (- \frac{3 z}{5}) = - \frac{5}{3} \cdot 9$

Step 4.1.1.1.2

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

$\frac{- 5}{3} \cdot \frac{- 3 z}{5} = - \frac{5}{3} \cdot 9$

Step 4.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{3} \cdot \frac{- 3 z}{5} = - \frac{5}{3} \cdot 9$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{3} \cdot \frac{- 3 z}{5} = - \frac{5}{3} \cdot 9$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 z) = - \frac{5}{3} \cdot 9$

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 $- 3 z$ .

$\frac{- 1}{3} (3 (- z)) = - \frac{5}{3} \cdot 9$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- z)) = - \frac{5}{3} \cdot 9$

Step 4.1.1.2.3

Rewrite the expression.

$- - z = - \frac{5}{3} \cdot 9$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 z = - \frac{5}{3} \cdot 9$

Step 4.1.1.3.2

Multiply $z$ by $1$ .

$z = - \frac{5}{3} \cdot 9$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{5}{3} \cdot 9$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

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

$z = \frac{- 5}{3} \cdot 9$

Step 4.2.1.1.2

Factor $3$ out of $9$ .

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

Step 4.2.1.1.3

Cancel the common factor.

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

Step 4.2.1.1.4

Rewrite the expression.

$z = - 5 \cdot 3$

Step 4.2.1.2

Multiply $- 5$ by $3$ .

$z = - 15$