Answer
$15$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=1}^5 (2x_i+3)
,$ 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}
(2x_1+3)+(2x_2+3)+(2x_3+3)+(2x_4+3)+(2x_5+3)
\\\\=
2x_1+3+2x_2+3+2x_3+3+2x_4+3+2x_5+3
\\\\=
(2x_1+2x_2+2x_3+2x_4+2x_5)+(3+3+3+3+3)
\\\\=
2(x_1+x_2+x_3+x_4+x_5)+15
.\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(-2+(-1)+0+1+2)+15
\\\\=
2(-2-1+0+1+2)+15
\\\\=
2(0)+15
\\\\=
0+15
\\\\=
15
.\end{array}
