Linear Algebra Examples

$x = - 3 y - 8$

Step 1

Rewrite the equation as $- 3 y - 8 = x$ .

$- 3 y - 8 = x$

Step 2

Add $8$ to both sides of the equation.

$- 3 y = x + 8$

Step 3

Divide each term in $- 3 y = x + 8$ by $- 3$ and simplify.

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Step 3.1

Divide each term in $- 3 y = x + 8$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{x}{- 3} + \frac{8}{- 3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{x}{- 3} + \frac{8}{- 3}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{x}{- 3} + \frac{8}{- 3}$

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

Move the negative in front of the fraction.

$y = - \frac{x}{3} + \frac{8}{- 3}$

Step 3.3.1.2

Move the negative in front of the fraction.

$y = - \frac{x}{3} - \frac{8}{3}$

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:

${x | x \in ℝ}$

Step 5