Calculus Examples

$z = 0.3 x + 1.5 y$

Step 1

Rewrite the equation as $0.3 x + 1.5 y = z$ .

$0.3 x + 1.5 y = z$

Step 2

Subtract $0.3 x$ from both sides of the equation.

$1.5 y = z - 0.3 x$

Step 3

Divide each term in $1.5 y = z - 0.3 x$ by $1.5$ and simplify.

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Step 3.1

Divide each term in $1.5 y = z - 0.3 x$ by $1.5$ .

$\frac{1.5 y}{1.5} = \frac{z}{1.5} + \frac{- 0.3 x}{1.5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $1.5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{1.5 y}{1.5} = \frac{z}{1.5} + \frac{- 0.3 x}{1.5}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{z}{1.5} + \frac{- 0.3 x}{1.5}$

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 by $1$ .

$y = \frac{1 z}{1.5} + \frac{- 0.3 x}{1.5}$

Step 3.3.1.2

Factor $1.5$ out of $1.5$ .

$y = \frac{1 z}{1.5 (1)} + \frac{- 0.3 x}{1.5}$

Step 3.3.1.3

Separate fractions.

$y = \frac{1}{1.5} \cdot \frac{z}{1} + \frac{- 0.3 x}{1.5}$

Step 3.3.1.4

Divide $1$ by $1.5$ .

$y = 0.\overline{6} \frac{z}{1} + \frac{- 0.3 x}{1.5}$

Step 3.3.1.5

Divide $z$ by $1$ .

$y = 0.\overline{6} z + \frac{- 0.3 x}{1.5}$

Step 3.3.1.6

Move the negative in front of the fraction.

$y = 0.\overline{6} z - \frac{0.3 x}{1.5}$

Step 3.3.1.7

Factor $0.3$ out of $0.3 x$ .

$y = 0.\overline{6} z - \frac{0.3 (x)}{1.5}$

Step 3.3.1.8

Factor $1.5$ out of $1.5$ .

$y = 0.\overline{6} z - \frac{0.3 (x)}{1.5 (1)}$

Step 3.3.1.9

Separate fractions.

$y = 0.\overline{6} z - (\frac{0.3}{1.5} \cdot \frac{x}{1})$

Step 3.3.1.10

Divide $0.3$ by $1.5$ .

$y = 0.\overline{6} z - (0.2 \frac{x}{1})$

Step 3.3.1.11

Cancel the common factor of $0.2$ .

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Step 3.3.1.11.1

Factor $0.2$ out of $1$ .

$y = 0.\overline{6} z - (0.2 \frac{x}{0.2 \cdot 5})$

Step 3.3.1.11.2

Cancel the common factor.

$y = 0.\overline{6} z - (0.2 \frac{x}{0.2 \cdot 5})$

Step 3.3.1.11.3

Rewrite the expression.

$y = 0.\overline{6} z - \frac{x}{5}$