Linear Algebra Examples

x = - 3 y - 8

$x = - 3 y - 8$

Step 1

Rewrite the equation as

- 3 y - 8 = x

$- 3 y - 8 = x$ .

- 3 y - 8 = x

$- 3 y - 8 = x$

Step 2

Add

8

$8$ to both sides of the equation.

- 3 y = x + 8

$- 3 y = x + 8$

Step 3

Divide each term in

- 3 y = x + 8

$- 3 y = x + 8$ by

- 3

$- 3$ and simplify.

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Step 3.1

Divide each term in

- 3 y = x + 8

$- 3 y = x + 8$ by

- 3

$- 3$ .

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

$x = - 3 y - 8$

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