Answer
$$125$$
Work Step by Step
$$\eqalign{
& \sum\limits_{j = 1}^{10} {\left( {3j - 4} \right)} \cr
& {\text{Use the summation properties}} \cr
& \sum\limits_{j = 1}^{10} {\left( {3j - 4} \right)} = \sum\limits_{j = 1}^{10} {3j - } \sum\limits_{j = 1}^{10} 4 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 3\sum\limits_{j = 1}^{10} {j - } \sum\limits_{j = 1}^{10} 4 \cr
& {\text{Use the properties }}\sum\limits_{i = 1}^n c = nc{\text{ and }}\sum\limits_{i = 1}^n i = \frac{{n\left( {n + 1} \right)}}{2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 3\left[ {\frac{{10\left( {10 + 1} \right)}}{2}} \right] - 4\left( {10} \right) \cr
& {\text{Simplifying}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 3\left[ {5\left( {10 + 1} \right)} \right] - 4\left( {10} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 165 - 40 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 125 \cr} $$
