Finite Math Examples

$x - (\frac{5}{2} x - \frac{9}{2})$

Step 1

Simplify each term.

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Step 1.1

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

$x - (\frac{5 x}{2} - \frac{9}{2})$

Step 1.2

Apply the distributive property.

$x - \frac{5 x}{2} - - \frac{9}{2}$

Step 1.3

Multiply $- - \frac{9}{2}$ .

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Step 1.3.1

Multiply $- 1$ by $- 1$ .

$x - \frac{5 x}{2} + 1 (\frac{9}{2})$

Step 1.3.2

Multiply $\frac{9}{2}$ by $1$ .

$x - \frac{5 x}{2} + \frac{9}{2}$

Step 2

To write $x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x \cdot \frac{2}{2} - \frac{5 x}{2} + \frac{9}{2}$

Step 3

Simplify terms.

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Step 3.1

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

$\frac{x \cdot 2}{2} - \frac{5 x}{2} + \frac{9}{2}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{x \cdot 2 - 5 x}{2} + \frac{9}{2}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{x \cdot 2 - 5 x + 9}{2}$

Step 4

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

$\frac{2 x - 5 x + 9}{2}$

Step 5

Simplify terms.

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Step 5.1

Subtract $5 x$ from $2 x$ .

$\frac{- 3 x + 9}{2}$

Step 5.2

Factor $3$ out of $- 3 x + 9$ .

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Step 5.2.1

Factor $3$ out of $- 3 x$ .

$\frac{3 (- x) + 9}{2}$

Step 5.2.2

Factor $3$ out of $9$ .

$\frac{3 (- x) + 3 (3)}{2}$

Step 5.2.3

Factor $3$ out of $3 (- x) + 3 (3)$ .

$\frac{3 (- x + 3)}{2}$

Step 5.3

Factor $- 1$ out of $- x$ .

$\frac{3 (- (x) + 3)}{2}$

Step 5.4

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{3 (- (x) - 1 (- 3))}{2}$

Step 5.5

Factor $- 1$ out of $- (x) - 1 (- 3)$ .

$\frac{3 (- (x - 3))}{2}$

Step 5.6

Simplify the expression.

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Step 5.6.1

Rewrite $- (x - 3)$ as $- 1 (x - 3)$ .

$\frac{3 (- 1 (x - 3))}{2}$

Step 5.6.2

Move the negative in front of the fraction.

$- \frac{3 (x - 3)}{2}$