Linear Algebra Examples

$- \frac{1}{4} x - 5$ , $\frac{3}{4} x - 9$

Step 1

Subtract the second expression $\frac{3}{4} x - 9$ from the first expression $- \frac{1}{4} x - 5$ .

$- \frac{1}{4} x - 5 - (\frac{3}{4} x - 9)$

Step 2

Simplify each term.

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Step 2.1

Combine $x$ and $\frac{1}{4}$ .

$- \frac{x}{4} - 5 - (\frac{3}{4} x - 9)$

Step 2.2

Combine $\frac{3}{4}$ and $x$ .

$- \frac{x}{4} - 5 - (\frac{3 x}{4} - 9)$

Step 2.3

Apply the distributive property.

$- \frac{x}{4} - 5 - \frac{3 x}{4} - - 9$

Step 2.4

Multiply $- 1$ by $- 9$ .

$- \frac{x}{4} - 5 - \frac{3 x}{4} + 9$

Step 3

Simplify terms.

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Step 3.1

Combine the numerators over the common denominator.

$- 5 + 9 + \frac{- x - 3 x}{4}$

Step 3.2

Subtract $3 x$ from $- x$ .

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

Step 3.3

Cancel the common factor of $- 4$ and $4$ .

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Step 3.3.1

Factor $4$ out of $- 4 x$ .

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

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $4$ out of $4$ .

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

Step 3.3.2.2

Cancel the common factor.

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

Step 3.3.2.3

Rewrite the expression.

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

Step 3.3.2.4

Divide $- x$ by $1$ .

$- 5 + 9 - x$

Step 3.4

Simplify the expression.

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Step 3.4.1

Add $- 5$ and $9$ .

$4 - x$

Step 3.4.2

Reorder $4$ and $- x$ .

$- x + 4$