Solve for a a=|(2(5-1)+8(1-1)+8(1-5))/2|

$a = | \frac{2 (5 - 1) + 8 (1 - 1) + 8 (1 - 5)}{2} |$

Step 1

Cancel the common factor of $2 (5 - 1) + 8 (1 - 1) + 8 (1 - 5)$ and $2$ .

Factor $2$ out of $8 (1 - 1)$ .

$a = | \frac{2 (5 - 1) + 2 (4 (1 - 1)) + 8 (1 - 5)}{2} |$

Factor $2$ out of $2 (5 - 1) + 2 (4 (1 - 1))$ .

$a = | \frac{2 (5 - 1 + 4 (1 - 1)) + 8 (1 - 5)}{2} |$

Factor $2$ out of $8 (1 - 5)$ .

$a = | \frac{2 (5 - 1 + 4 (1 - 1)) + 2 (4 (1 - 5))}{2} |$

Factor $2$ out of $2 (5 - 1 + 4 (1 - 1)) + 2 (4 (1 - 5))$ .

$a = | \frac{2 (5 - 1 + 4 (1 - 1) + 4 (1 - 5))}{2} |$

Cancel the common factors.

Factor $2$ out of $2$ .

$a = | \frac{2 (5 - 1 + 4 (1 - 1) + 4 (1 - 5))}{2 (1)} |$

Cancel the common factor.

$a = | \frac{2 (5 - 1 + 4 (1 - 1) + 4 (1 - 5))}{2 \cdot 1} |$

Rewrite the expression.

$a = | \frac{5 - 1 + 4 (1 - 1) + 4 (1 - 5)}{1} |$

Divide $5 - 1 + 4 (1 - 1) + 4 (1 - 5)$ by $1$ .

$a = | 5 - 1 + 4 (1 - 1) + 4 (1 - 5) |$

Step 2

Simplify each term.

Subtract $1$ from $1$ .

$a = | 5 - 1 + 4 \cdot 0 + 4 (1 - 5) |$

Multiply $4$ by $0$ .

$a = | 5 - 1 + 0 + 4 (1 - 5) |$

Subtract $5$ from $1$ .

$a = | 5 - 1 + 0 + 4 \cdot - 4 |$

Multiply $4$ by $- 4$ .

$a = | 5 - 1 + 0 - 16 |$

Step 3

Simplify by adding and subtracting.

Subtract $1$ from $5$ .

$a = | 4 + 0 - 16 |$

Add $4$ and $0$ .

$a = | 4 - 16 |$

Subtract $16$ from $4$ .

$a = | - 12 |$

Step 4

The absolute value is the distance between a number and zero. The distance between $- 12$ and $0$ is $12$ .

$a = 12$