Finite Math Examples

$z = 1.5 x + 0.75 y$

Step 1

Rewrite the equation as $1.5 x + 0.75 y = z$ .

$1.5 x + 0.75 y = z$

Step 2

Subtract $1.5 x$ from both sides of the equation.

$0.75 y = z - 1.5 x$

Step 3

Divide each term in $0.75 y = z - 1.5 x$ by $0.75$ and simplify.

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Step 3.1

Divide each term in $0.75 y = z - 1.5 x$ by $0.75$ .

$\frac{0.75 y}{0.75} = \frac{z}{0.75} + \frac{- 1.5 x}{0.75}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.75$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.75 y}{0.75} = \frac{z}{0.75} + \frac{- 1.5 x}{0.75}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{z}{0.75} + \frac{- 1.5 x}{0.75}$

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 $1$ .

$y = \frac{1 z}{0.75} + \frac{- 1.5 x}{0.75}$

Step 3.3.1.2

Factor $0.75$ out of $0.75$ .

$y = \frac{1 z}{0.75 (1)} + \frac{- 1.5 x}{0.75}$

Step 3.3.1.3

Separate fractions.

$y = \frac{1}{0.75} \cdot \frac{z}{1} + \frac{- 1.5 x}{0.75}$

Step 3.3.1.4

Divide $1$ by $0.75$ .

$y = 1.\overline{3} \frac{z}{1} + \frac{- 1.5 x}{0.75}$

Step 3.3.1.5

Divide $z$ by $1$ .

$y = 1.\overline{3} z + \frac{- 1.5 x}{0.75}$

Step 3.3.1.6

Move the negative in front of the fraction.

$y = 1.\overline{3} z - \frac{1.5 x}{0.75}$

Step 3.3.1.7

Factor $1.5$ out of $1.5 x$ .

$y = 1.\overline{3} z - \frac{1.5 (x)}{0.75}$

Step 3.3.1.8

Factor $0.75$ out of $0.75$ .

$y = 1.\overline{3} z - \frac{1.5 (x)}{0.75 (1)}$

Step 3.3.1.9

Separate fractions.

$y = 1.\overline{3} z - (\frac{1.5}{0.75} \cdot \frac{x}{1})$

Step 3.3.1.10

Divide $1.5$ by $0.75$ .

$y = 1.\overline{3} z - (2 \frac{x}{1})$

Step 3.3.1.11

Divide $x$ by $1$ .

$y = 1.\overline{3} z - (2 x)$

Step 3.3.1.12

Multiply $2$ by $- 1$ .

$y = 1.\overline{3} z - 2 x$

Step 4

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$