Linear Algebra Examples

$x - 1.5 y = - 1.6$

Step 1

Subtract $x$ from both sides of the equation.

$- 1.5 y = - 1.6 - x$

Step 2

Divide each term in $- 1.5 y = - 1.6 - x$ by $- 1.5$ and simplify.

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Step 2.1

Divide each term in $- 1.5 y = - 1.6 - x$ by $- 1.5$ .

$\frac{- 1.5 y}{- 1.5} = \frac{- 1.6}{- 1.5} + \frac{- x}{- 1.5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 1.5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 1.5 y}{- 1.5} = \frac{- 1.6}{- 1.5} + \frac{- x}{- 1.5}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 1.6}{- 1.5} + \frac{- x}{- 1.5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $- 1.6$ by $- 1.5$ .

$y = 1.0\overline{6} + \frac{- x}{- 1.5}$

Step 2.3.1.2

Dividing two negative values results in a positive value.

$y = 1.0\overline{6} + \frac{x}{1.5}$

Step 2.3.1.3

Multiply by $1$ .

$y = 1.0\overline{6} + \frac{1 x}{1.5}$

Step 2.3.1.4

Factor $1.5$ out of $1.5$ .

$y = 1.0\overline{6} + \frac{1 x}{1.5 (1)}$

Step 2.3.1.5

Separate fractions.

$y = 1.0\overline{6} + \frac{1}{1.5} \cdot \frac{x}{1}$

Step 2.3.1.6

Divide $1$ by $1.5$ .

$y = 1.0\overline{6} + 0.\overline{6} \frac{x}{1}$

Step 2.3.1.7

Divide $x$ by $1$ .

$y = 1.0\overline{6} + 0.\overline{6} x$

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:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4