Answer
$-2$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=1}^4 (-3x_i-2)
,$ substitute $ i $ with the values from $ 1 $ to $ 4 .$ 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}
(-3x_1-2)+(-3x_2-2)+(-3x_3-2)+(-3x_4-2)
\\\\=
-3x_1-2-3x_2-2-3x_3-2-3x_4-2
\\\\=
(-3x_1-3x_2-3x_3-3x_4)+(-2-2-2-2)
\\\\=
(-3x_1-3x_2-3x_3-3x_4)+(-8)
\\\\=
(-3x_1-3x_2-3x_3-3x_4)-8
.\end{array}
Factoring the common factor, $-3,$ in the expression $(-3x_1-3x_2-3x_3-3x_4-3x_5),$ results to \begin{array}{l}\require{cancel}
-3(x_1+x_2+x_3+x_4)-8
.\end{array}
Using the given values $x_1=-2,x_2=-1,x_3=0,$ and $x_4=1,$ the expression above evaluates to \begin{array}{l}\require{cancel}
-3(-2+(-1)+0+1)-8
\\\\=
-3(-2-1+0+1)-8
\\\\=
-3(-2)-8
\\\\=
6-8
\\\\=
-2
.\end{array}