Linear Algebra Examples

$x + \frac{5}{2} x + 10.25 x = 48.75$

Step 1

Simplify $x + \frac{5}{2} x + 10.25 x$ .

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Step 1.1

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

$x + \frac{5 x}{2} + 10.25 x = 48.75$

Step 1.2

Find the common denominator.

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Step 1.2.1

Write $x$ as a fraction with denominator $1$ .

$\frac{x}{1} + \frac{5 x}{2} + 10.25 x = 48.75$

Step 1.2.2

Multiply $\frac{x}{1}$ by $\frac{2}{2}$ .

$\frac{x}{1} \cdot \frac{2}{2} + \frac{5 x}{2} + 10.25 x = 48.75$

Step 1.2.3

Multiply $\frac{x}{1}$ by $\frac{2}{2}$ .

$\frac{x \cdot 2}{2} + \frac{5 x}{2} + 10.25 x = 48.75$

Step 1.2.4

Write $10.25 x$ as a fraction with denominator $1$ .

$\frac{x \cdot 2}{2} + \frac{5 x}{2} + \frac{10.25 x}{1} = 48.75$

Step 1.2.5

Multiply $\frac{10.25 x}{1}$ by $\frac{2}{2}$ .

$\frac{x \cdot 2}{2} + \frac{5 x}{2} + \frac{10.25 x}{1} \cdot \frac{2}{2} = 48.75$

Step 1.2.6

Multiply $\frac{10.25 x}{1}$ by $\frac{2}{2}$ .

$\frac{x \cdot 2}{2} + \frac{5 x}{2} + \frac{10.25 x \cdot 2}{2} = 48.75$

Step 1.3

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 5 x + 10.25 x \cdot 2}{2} = 48.75$

Step 1.4

Simplify each term.

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Step 1.4.1

Move $2$ to the left of $x$ .

$\frac{2 \cdot x + 5 x + 10.25 x \cdot 2}{2} = 48.75$

Step 1.4.2

Multiply $2$ by $10.25$ .

$\frac{2 x + 5 x + 20.5 x}{2} = 48.75$

Step 1.5

Simplify terms.

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Step 1.5.1

Add $2 x$ and $5 x$ .

$\frac{7 x + 20.5 x}{2} = 48.75$

Step 1.5.2

Add $7 x$ and $20.5 x$ .

$\frac{27.5 x}{2} = 48.75$

Step 1.5.3

Factor $27.5$ out of $27.5 x$ .

$\frac{27.5 (x)}{2} = 48.75$

Step 1.5.4

Factor $2$ out of $2$ .

$\frac{27.5 (x)}{2 (1)} = 48.75$

Step 1.6

Separate fractions.

$\frac{27.5}{2} \cdot \frac{x}{1} = 48.75$

Step 1.7

Divide $27.5$ by $2$ .

$13.75 \frac{x}{1} = 48.75$

Step 1.8

Divide $x$ by $1$ .

$13.75 x = 48.75$

Step 2

Divide each term in $13.75 x = 48.75$ by $13.75$ and simplify.

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Step 2.1

Divide each term in $13.75 x = 48.75$ by $13.75$ .

$\frac{13.75 x}{13.75} = \frac{48.75}{13.75}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $13.75$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{13.75 x}{13.75} = \frac{48.75}{13.75}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{48.75}{13.75}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $48.75$ by $13.75$ .

$x = 3.\overline{54}$

Step 3

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

${x | x = 3.\overline{54}}$

Step 4