Linear Algebra Examples

$\frac{4}{5} x = 6$

Step 1

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

$\frac{5}{4} (\frac{4}{5} x) = \frac{5}{4} \cdot 6$

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 $x$ .

$\frac{5}{4} \cdot \frac{4 x}{5} = \frac{5}{4} \cdot 6$

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.

$\frac{5}{4} \cdot \frac{4 x}{5} = \frac{5}{4} \cdot 6$

Step 2.1.1.2.2

Rewrite the expression.

$\frac{1}{4} (4 x) = \frac{5}{4} \cdot 6$

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 $4 x$ .

$\frac{1}{4} (4 (x)) = \frac{5}{4} \cdot 6$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{1}{4} (4 x) = \frac{5}{4} \cdot 6$

Step 2.1.1.3.3

Rewrite the expression.

$x = \frac{5}{4} \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{5}{4} \cdot 6$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $4$ .

$x = \frac{5}{2 (2)} \cdot 6$

Step 2.2.1.1.2

Factor $2$ out of $6$ .

$x = \frac{5}{2 \cdot 2} \cdot (2 \cdot 3)$

Step 2.2.1.1.3

Cancel the common factor.

$x = \frac{5}{2 \cdot 2} \cdot (2 \cdot 3)$

Step 2.2.1.1.4

Rewrite the expression.

$x = \frac{5}{2} \cdot 3$

Step 2.2.1.2

Combine $\frac{5}{2}$ and $3$ .

$x = \frac{5 \cdot 3}{2}$

Step 2.2.1.3

Multiply $5$ by $3$ .

$x = \frac{15}{2}$

Step 3

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

${x | x = \frac{15}{2}}$

Step 4