Algebra Examples

$- (- 2 u + 8) - \frac{3}{4} u$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- (- 2 u) - 1 \cdot 8 - \frac{3}{4} u$

Step 1.2

Multiply $- 2$ by $- 1$ .

$2 u - 1 \cdot 8 - \frac{3}{4} u$

Step 1.3

Multiply $- 1$ by $8$ .

$2 u - 8 - \frac{3}{4} u$

Step 1.4

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

$2 u - 8 - \frac{u \cdot 3}{4}$

Step 1.5

Move $3$ to the left of $u$ .

$2 u - 8 - \frac{3 u}{4}$

Step 2

To write $2 u$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$2 u \cdot \frac{4}{4} - \frac{3 u}{4} - 8$

Step 3

Simplify terms.

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Step 3.1

Combine $2 u$ and $\frac{4}{4}$ .

$\frac{2 u \cdot 4}{4} - \frac{3 u}{4} - 8$

Step 3.2

Combine the numerators over the common denominator.

$\frac{2 u \cdot 4 - 3 u}{4} - 8$

Step 4

Simplify each term.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Factor $u$ out of $2 u \cdot 4 - 3 u$ .

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Step 4.1.1.1

Factor $u$ out of $2 u \cdot 4$ .

$\frac{u (2 \cdot 4) - 3 u}{4} - 8$

Step 4.1.1.2

Factor $u$ out of $- 3 u$ .

$\frac{u (2 \cdot 4) + u \cdot - 3}{4} - 8$

Step 4.1.1.3

Factor $u$ out of $u (2 \cdot 4) + u \cdot - 3$ .

$\frac{u (2 \cdot 4 - 3)}{4} - 8$

Step 4.1.2

Multiply $2$ by $4$ .

$\frac{u (8 - 3)}{4} - 8$

Step 4.1.3

Subtract $3$ from $8$ .

$\frac{u \cdot 5}{4} - 8$

Step 4.2

Move $5$ to the left of $u$ .

$\frac{5 u}{4} - 8$