Linear Algebra Examples

$x = 3 y + 1$

Step 1

Rewrite the equation as $3 y + 1 = x$ .

$3 y + 1 = x$

Step 2

Subtract $1$ from both sides of the equation.

$3 y = x - 1$

Step 3

Divide each term in $3 y = x - 1$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 y = x - 1$ by $3$ .

$\frac{3 y}{3} = \frac{x}{3} + \frac{- 1}{3}$

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.

$\frac{3 y}{3} = \frac{x}{3} + \frac{- 1}{3}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{x}{3} + \frac{- 1}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$y = \frac{x}{3} - \frac{1}{3}$

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