Linear Algebra Examples

$1 = - \frac{5}{9} x + 5$

Step 1

Rewrite the equation as $- \frac{5}{9} x + 5 = 1$ .

$- \frac{5}{9} x + 5 = 1$

Step 2

Simplify each term.

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Step 2.1

Combine $x$ and $\frac{5}{9}$ .

$- \frac{x \cdot 5}{9} + 5 = 1$

Step 2.2

Move $5$ to the left of $x$ .

$- \frac{5 x}{9} + 5 = 1$

Step 3

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1

Subtract $5$ from both sides of the equation.

$- \frac{5 x}{9} = 1 - 5$

Step 3.2

Subtract $5$ from $1$ .

$- \frac{5 x}{9} = - 4$

Step 4

Multiply both sides of the equation by $- \frac{9}{5}$ .

$- \frac{9}{5} (- \frac{5 x}{9}) = - \frac{9}{5} \cdot - 4$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{9}{5} (- \frac{5 x}{9})$ .

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Step 5.1.1.1

Cancel the common factor of $9$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$\frac{- 9}{5} (- \frac{5 x}{9}) = - \frac{9}{5} \cdot - 4$

Step 5.1.1.1.2

Move the leading negative in $- \frac{5 x}{9}$ into the numerator.

$\frac{- 9}{5} \cdot \frac{- 5 x}{9} = - \frac{9}{5} \cdot - 4$

Step 5.1.1.1.3

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{5} \cdot \frac{- 5 x}{9} = - \frac{9}{5} \cdot - 4$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{9 \cdot - 1}{5} \cdot \frac{- 5 x}{9} = - \frac{9}{5} \cdot - 4$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 x) = - \frac{9}{5} \cdot - 4$

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $- 5 x$ .

$\frac{- 1}{5} (5 (- x)) = - \frac{9}{5} \cdot - 4$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- x)) = - \frac{9}{5} \cdot - 4$

Step 5.1.1.2.3

Rewrite the expression.

$- - x = - \frac{9}{5} \cdot - 4$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{9}{5} \cdot - 4$

Step 5.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{9}{5} \cdot - 4$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- \frac{9}{5} \cdot - 4$ .

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Step 5.2.1.1

Multiply $- 4$ by $- 1$ .

$x = 4 (\frac{9}{5})$

Step 5.2.1.2

Combine $4$ and $\frac{9}{5}$ .

$x = \frac{4 \cdot 9}{5}$

Step 5.2.1.3

Multiply $4$ by $9$ .

$x = \frac{36}{5}$

Step 6

The domain is the set of all valid $x$ values.

${x | x = \frac{36}{5}}$

Step 7