Finite Math Examples

$6 y - 9 x = 7$

Step 1

Add $9 x$ to both sides of the equation.

$6 y = 7 + 9 x$

Step 2

Divide each term in $6 y = 7 + 9 x$ by $6$ and simplify.

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Step 2.1

Divide each term in $6 y = 7 + 9 x$ by $6$ .

$\frac{6 y}{6} = \frac{7}{6} + \frac{9 x}{6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{7}{6} + \frac{9 x}{6}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{7}{6} + \frac{9 x}{6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $9$ and $6$ .

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Step 2.3.1.1

Factor $3$ out of $9 x$ .

$y = \frac{7}{6} + \frac{3 (3 x)}{6}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $3$ out of $6$ .

$y = \frac{7}{6} + \frac{3 (3 x)}{3 (2)}$

Step 2.3.1.2.2

Cancel the common factor.

$y = \frac{7}{6} + \frac{3 (3 x)}{3 \cdot 2}$

Step 2.3.1.2.3

Rewrite the expression.

$y = \frac{7}{6} + \frac{3 x}{2}$

Step 3

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 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 5

Determine the domain and range.

Domain: $(- \infty, \infty), {x | x \in ℝ}$

Range: $(- \infty, \infty), {y | y \in ℝ}$

Step 6