Linear Algebra Examples

$\frac{x}{7} = \frac{15}{21}$

Step 1

Multiply both sides of the equation by $7$ .

$7 \frac{x}{7} = 7 (\frac{15}{21})$

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

Cancel the common factor of $7$ .

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Step 2.1.1.1

Cancel the common factor.

$7 \frac{x}{7} = 7 (\frac{15}{21})$

Step 2.1.1.2

Rewrite the expression.

$x = 7 (\frac{15}{21})$

$x = 7 (\frac{15}{21})$

$x = 7 (\frac{15}{21})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $7 (\frac{15}{21})$ .

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Step 2.2.1.1

Cancel the common factor of $7$ .

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Step 2.2.1.1.1

Factor $7$ out of $21$ .

$x = 7 \frac{15}{7 (3)}$

Step 2.2.1.1.2

Cancel the common factor.

$x = 7 \frac{15}{7 \cdot 3}$

Step 2.2.1.1.3

Rewrite the expression.

$x = \frac{15}{3}$

$x = \frac{15}{3}$

Step 2.2.1.2

Divide $15$ by $3$ .

$x = 5$

$x = 5$

$x = 5$

$x = 5$

Step 3

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

${x | x = 5}$

Step 4

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$