Answer
$$\left\{ {13} \right\}$$
Work Step by Step
$$\eqalign{
& \left| {\matrix{
5 & {3x} & { - 3} \cr
0 & 2 & { - 1} \cr
4 & { - 1} & x \cr
} } \right| = - 7 \cr
& {\rm{Expand \,the\, determinant \,to\, obtain}} \cr
& - 0 + 2\left| {\matrix{
5 & { - 3} \cr
4 & x \cr
} } \right| - \left( { - 1} \right)\left| {\matrix{
5 & {3x} \cr
4 & { - 1} \cr
} } \right| = - 7 \cr
& 2\left( {5x + 12} \right) + \left( { - 5 - 12x} \right) = - 7 \cr
& {\rm{Solve\, the\, equation}} \cr
& 10x + 24 - 5 - 12x = - 7 \cr
& - 2x + 19 = - 7 \cr
& - 2x = - 26 \cr
& x = 13 \cr
& {\rm{The\, solution\, set\, is}} \cr
& \left\{ {13} \right\} \cr} $$
