Answer
$0$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=1}^5 -x_i
,$ substitute $
i
$ with the values from $
1
$ to $
5
.$ Then substitute the given values for each $x_i$'s
$\bf{\text{Solution Details:}}$
Substituting $
i
$ with the numbers from $
1
$ to $
5
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
-x_1+(-x_2)+(-x_3)+(-x_4)+(-x_5)
\\\\=
-x_1-x_2-x_3-x_4-x_5
.\end{array}
Using the given values $x_1=-2,x_2=-1,x_3=0,x_4=1,$ and $x_5=2,$ the expression above evaluates to
\begin{array}{l}\require{cancel}
-(-2)-(-1)-0-1-2
\\\\=
2+1-0-1-2
\\\\=
0
.\end{array}
