Finite Math Examples

$2 x - 5 y = 32$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $2 x$ from both sides of the equation.

$- 5 y = 32 - 2 x$

Step 1.2

Divide each term in $- 5 y = 32 - 2 x$ by $- 5$ and simplify.

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Step 1.2.1

Divide each term in $- 5 y = 32 - 2 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{32}{- 5} + \frac{- 2 x}{- 5}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 5$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{32}{- 5} + \frac{- 2 x}{- 5}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{32}{- 5} + \frac{- 2 x}{- 5}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Move the negative in front of the fraction.

$y = - \frac{32}{5} + \frac{- 2 x}{- 5}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{32}{5} + \frac{2 x}{5}$

Step 2

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:

${x | x \in ℝ}$

Step 3

Since the domain is all real numbers, $- \frac{32}{5} + \frac{2 x}{5}$ is continuous over all real numbers.

Continuous

Step 4