The problem requires us to evaluate the given expressions involving absolute values. The expressions are: a) $|-2|$ b) $|-8|$ c) $-|3|$ d) $|-3+0|$ e) $-|-1-2|$

1. Problem Description

The problem requires us to evaluate the given expressions involving absolute values. The expressions are:

a) $|-2|$

b) $|-8|$

c) $-|3|$

d) $|-3+0|$

e) $-|-1-2|$

2. Solution Steps

a) The absolute value of $-2$ is the distance from $-2$ to $0$, which is $2$.

$|-2| = 2$

b) The absolute value of $-8$ is the distance from $-8$ to $0$, which is $8$.

$|-8| = 8$

c) The absolute value of $3$ is $3$, so $-|3|$ is $-3$.

$-|3| = -3$

d) First, simplify inside the absolute value: $-3 + 0 = -3$. The absolute value of $-3$ is the distance from $-3$ to $0$, which is $3$.

$|-3 + 0| = |-3| = 3$

e) First, simplify inside the inner absolute value: $-1-2 = -3$. The absolute value of $-3$ is $3$. Then we take the negative of that result.

$-|-1-2| = -|-3| = -3$

3. Final Answer

a) 2

b) 8

c) -3

d) 3

e) -3