2x - 1 ≤ 2(2x + 4)
2x - 1 ≤ 4x + 8
-1 - 8 ≤ 4x - 2x
-9 ≤ 2x
x ≥ -4.5

0.6^(2 + 3x) > (5/3)^x
0.6^2 0.6^(3x) > (5/3)^x
0.36 0.6^(3x) > (5/3)^x
0.6^(3x) > (5/3)^x / 0.36
0.6^(3x) > (5/3)^x / 0.36
(2/3)^(3x) > (5/3)^x / 0.36
(2/3)^(3x) > (5/3)^x / 0.36
3x > x log(5/3) - log(0.36)
3x - x > log(5/3) - log(0.36)
2x > log(5/3) - log(0.36)
x > (log(5/3) - log(0.36))/2

Therefore, the solution to the system of inequalities is x ≥ -4.5 and x > (log(5/3) - log(0.36))/2.