Linear Algebra Examples

$x = y + 0.25 y$

Step 1

Rewrite the equation as $y + 0.25 y = x$ .

$y + 0.25 y = x$

Step 2

Add $y$ and $0.25 y$ .

$1.25 y = x$

Step 3

Divide each term in $1.25 y = x$ by $1.25$ and simplify.

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Step 3.1

Divide each term in $1.25 y = x$ by $1.25$ .

$\frac{1.25 y}{1.25} = \frac{x}{1.25}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $1.25$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{1.25 y}{1.25} = \frac{x}{1.25}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{x}{1.25}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply by $1$ .

$y = \frac{1 x}{1.25}$

Step 3.3.2

Factor $1.25$ out of $1.25$ .

$y = \frac{1 x}{1.25 (1)}$

Step 3.3.3

Separate fractions.

$y = \frac{1}{1.25} \cdot \frac{x}{1}$

Step 3.3.4

Divide $1$ by $1.25$ .

$y = 0.8 \frac{x}{1}$

Step 3.3.5

Divide $x$ by $1$ .

$y = 0.8 x$

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