Linear Algebra Examples

$\frac{4}{5} x = 36$

Step 1

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} (\frac{4}{5} x) = \frac{5}{4} \cdot 36$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{5}{4} (\frac{4}{5} x)$ .

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Step 2.1.1.1

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

$\frac{5}{4} \cdot \frac{4 x}{5} = \frac{5}{4} \cdot 36$

Step 2.1.1.2

Cancel the common factor of $5$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 x}{5} = \frac{5}{4} \cdot 36$

Step 2.1.1.2.2

Rewrite the expression.

$\frac{1}{4} (4 x) = \frac{5}{4} \cdot 36$

Step 2.1.1.3

Cancel the common factor of $4$ .

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Step 2.1.1.3.1

Factor $4$ out of $4 x$ .

$\frac{1}{4} (4 (x)) = \frac{5}{4} \cdot 36$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{1}{4} (4 x) = \frac{5}{4} \cdot 36$

Step 2.1.1.3.3

Rewrite the expression.

$x = \frac{5}{4} \cdot 36$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{5}{4} \cdot 36$ .

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Step 2.2.1.1

Cancel the common factor of $4$ .

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Step 2.2.1.1.1

Factor $4$ out of $36$ .

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

Step 2.2.1.1.2

Cancel the common factor.

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

Step 2.2.1.1.3

Rewrite the expression.

$x = 5 \cdot 9$

Step 2.2.1.2

Multiply $5$ by $9$ .

$x = 45$

Step 3

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

${x | x = 45}$

Step 4