Algebra Examples

$(- \frac{11}{2} x + 3) - 2 (- \frac{11}{4} x - \frac{5}{2})$

Step 1

Simplify each term.

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Step 1.1

Combine $x$ and $\frac{11}{2}$ .

$- \frac{x \cdot 11}{2} + 3 - 2 (- \frac{11}{4} x - \frac{5}{2})$

Step 1.2

Move $11$ to the left of $x$ .

$- \frac{11 \cdot x}{2} + 3 - 2 (- \frac{11}{4} x - \frac{5}{2})$

Step 1.3

Simplify each term.

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Step 1.3.1

Combine $x$ and $\frac{11}{4}$ .

$- \frac{11 x}{2} + 3 - 2 (- \frac{x \cdot 11}{4} - \frac{5}{2})$

Step 1.3.2

Move $11$ to the left of $x$ .

$- \frac{11 x}{2} + 3 - 2 (- \frac{11 x}{4} - \frac{5}{2})$

Step 1.4

Apply the distributive property.

$- \frac{11 x}{2} + 3 - 2 (- \frac{11 x}{4}) - 2 (- \frac{5}{2})$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Move the leading negative in $- \frac{11 x}{4}$ into the numerator.

$- \frac{11 x}{2} + 3 - 2 \frac{- 11 x}{4} - 2 (- \frac{5}{2})$

Step 1.5.2

Factor $2$ out of $- 2$ .

$- \frac{11 x}{2} + 3 + 2 (- 1) \frac{- 11 x}{4} - 2 (- \frac{5}{2})$

Step 1.5.3

Factor $2$ out of $4$ .

$- \frac{11 x}{2} + 3 + 2 \cdot - 1 \frac{- 11 x}{2 \cdot 2} - 2 (- \frac{5}{2})$

Step 1.5.4

Cancel the common factor.

$- \frac{11 x}{2} + 3 + 2 \cdot - 1 \frac{- 11 x}{2 \cdot 2} - 2 (- \frac{5}{2})$

Step 1.5.5

Rewrite the expression.

$- \frac{11 x}{2} + 3 - 1 \frac{- 11 x}{2} - 2 (- \frac{5}{2})$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$- \frac{11 x}{2} + 3 - 1 \frac{- 11 x}{2} - 2 (\frac{- 5}{2})$

Step 1.6.2

Factor $2$ out of $- 2$ .

$- \frac{11 x}{2} + 3 - 1 \frac{- 11 x}{2} + 2 (- 1) \frac{- 5}{2}$

Step 1.6.3

Cancel the common factor.

$- \frac{11 x}{2} + 3 - 1 \frac{- 11 x}{2} + 2 \cdot - 1 \frac{- 5}{2}$

Step 1.6.4

Rewrite the expression.

$- \frac{11 x}{2} + 3 - 1 \frac{- 11 x}{2} - 1 \cdot - 5$

Step 1.7

Multiply $- 1$ by $- 5$ .

$- \frac{11 x}{2} + 3 - 1 \frac{- 11 x}{2} + 5$

Step 1.8

Simplify each term.

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Step 1.8.1

Move the negative in front of the fraction.

$- \frac{11 x}{2} + 3 - 1 (- \frac{11 x}{2}) + 5$

Step 1.8.2

Multiply $- 1 (- \frac{11 x}{2})$ .

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Step 1.8.2.1

Multiply $- 1$ by $- 1$ .

$- \frac{11 x}{2} + 3 + 1 \frac{11 x}{2} + 5$

Step 1.8.2.2

Multiply $\frac{11 x}{2}$ by $1$ .

$- \frac{11 x}{2} + 3 + \frac{11 x}{2} + 5$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $- \frac{11 x}{2} + 3 + \frac{11 x}{2} + 5$ .

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Step 2.1.1

Add $- \frac{11 x}{2}$ and $\frac{11 x}{2}$ .

$0 + 3 + 5$

Step 2.1.2

Add $0$ and $3$ .

$3 + 5$

Step 2.2

Add $3$ and $5$ .

$8$