Linear Algebra Examples

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

Step 1

Divide each term in $3 y = \frac{3}{2} x + 6$ by $3$ and simplify.

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Step 1.1

Divide each term in $3 y = \frac{3}{2} x + 6$ by $3$ .

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

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $3$ .

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Step 1.2.1.1

Cancel the common factor.

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

Step 1.2.1.2

Divide $y$ by $1$ .

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

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Combine $\frac{3}{2}$ and $x$ .

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

Step 1.3.1.2

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{3 x}{2} \cdot \frac{1}{3} + \frac{6}{3}$

Step 1.3.1.3

Cancel the common factor of $3$ .

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Step 1.3.1.3.1

Factor $3$ out of $3 x$ .

$y = \frac{3 (x)}{2} \cdot \frac{1}{3} + \frac{6}{3}$

Step 1.3.1.3.2

Cancel the common factor.

$y = \frac{3 x}{2} \cdot \frac{1}{3} + \frac{6}{3}$

Step 1.3.1.3.3

Rewrite the expression.

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

Step 1.3.1.4

Divide $6$ by $3$ .

$y = \frac{x}{2} + 2$

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