Linear Algebra Examples

$10 y = 16 x - 5$

Step 1

Divide each term in $10 y = 16 x - 5$ by $10$ and simplify.

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Step 1.1

Divide each term in $10 y = 16 x - 5$ by $10$ .

$\frac{10 y}{10} = \frac{16 x}{10} + \frac{- 5}{10}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $10$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{10 y}{10} = \frac{16 x}{10} + \frac{- 5}{10}$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{16 x}{10} + \frac{- 5}{10}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Cancel the common factor of $16$ and $10$ .

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Step 1.3.1.1.1

Factor $2$ out of $16 x$ .

$y = \frac{2 (8 x)}{10} + \frac{- 5}{10}$

Step 1.3.1.1.2

Cancel the common factors.

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Step 1.3.1.1.2.1

Factor $2$ out of $10$ .

$y = \frac{2 (8 x)}{2 (5)} + \frac{- 5}{10}$

Step 1.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (8 x)}{2 \cdot 5} + \frac{- 5}{10}$

Step 1.3.1.1.2.3

Rewrite the expression.

$y = \frac{8 x}{5} + \frac{- 5}{10}$

Step 1.3.1.2

Cancel the common factor of $- 5$ and $10$ .

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Step 1.3.1.2.1

Factor $5$ out of $- 5$ .

$y = \frac{8 x}{5} + \frac{5 (- 1)}{10}$

Step 1.3.1.2.2

Cancel the common factors.

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Step 1.3.1.2.2.1

Factor $5$ out of $10$ .

$y = \frac{8 x}{5} + \frac{5 \cdot - 1}{5 \cdot 2}$

Step 1.3.1.2.2.2

Cancel the common factor.

$y = \frac{8 x}{5} + \frac{5 \cdot - 1}{5 \cdot 2}$

Step 1.3.1.2.2.3

Rewrite the expression.

$y = \frac{8 x}{5} + \frac{- 1}{2}$

Step 1.3.1.3

Move the negative in front of the fraction.

$y = \frac{8 x}{5} - \frac{1}{2}$

Step 2

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 3