Linear Algebra Examples

5 x - y = 38

$5 x - y = 38$

Step 1

Subtract

5 x

$5 x$ from both sides of the equation.

- y = 38 - 5 x

$- y = 38 - 5 x$

Step 2

Divide each term in

- y = 38 - 5 x

$- y = 38 - 5 x$ by

- 1

$- 1$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in

- y = 38 - 5 x

$- y = 38 - 5 x$ by

- 1

$- 1$ .

\frac{- y}{- 1} = \frac{38}{- 1} + \frac{- 5 x}{- 1}

$\frac{- y}{- 1} = \frac{38}{- 1} + \frac{- 5 x}{- 1}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Dividing two negative values results in a positive value.

\frac{y}{1} = \frac{38}{- 1} + \frac{- 5 x}{- 1}

$\frac{y}{1} = \frac{38}{- 1} + \frac{- 5 x}{- 1}$

Step 2.2.2

Divide

y

$y$ by

1

$1$ .

y = \frac{38}{- 1} + \frac{- 5 x}{- 1}

$y = \frac{38}{- 1} + \frac{- 5 x}{- 1}$

y = \frac{38}{- 1} + \frac{- 5 x}{- 1}

$y = \frac{38}{- 1} + \frac{- 5 x}{- 1}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Simplify each term.

Tap for more steps...

Step 2.3.1.1

Divide

38

$38$ by

- 1

$- 1$ .

y = - 38 + \frac{- 5 x}{- 1}

$y = - 38 + \frac{- 5 x}{- 1}$

Step 2.3.1.2

Move the negative one from the denominator of

\frac{- 5 x}{- 1}

$\frac{- 5 x}{- 1}$ .

y = - 38 - 1 \cdot (- 5 x)

$y = - 38 - 1 \cdot (- 5 x)$

Step 2.3.1.3

Rewrite

- 1 \cdot (- 5 x)

$- 1 \cdot (- 5 x)$ as

- (- 5 x)

$- (- 5 x)$ .

y = - 38 - (- 5 x)

$y = - 38 - (- 5 x)$

Step 2.3.1.4

Multiply

- 5

$- 5$ by

- 1

$- 1$ .

y = - 38 + 5 x

$y = - 38 + 5 x$

y = - 38 + 5 x

$y = - 38 + 5 x$

y = - 38 + 5 x

$y = - 38 + 5 x$

y = - 38 + 5 x

$y = - 38 + 5 x$

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)

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4