3^1/(5x -2 ) ≤ (1/3)^1/(5 - 3x)
3^1/(5x - 2) ≤ 3^[- 1/(5 - 3x)]
3 > 1
1/(5x - 2) ≤ - 1/(5 - 3x)]
1/(5x - 2) + 1/(5 - 3x) ≤ 0
{(5 - 3x + 5x - 2) / [(5x - 2)*(5 - 3x)]} ≤ 0
{(3 + 2x) / [(5x - 2)*(5 - 3x)]} ≤ 0
ОДЗ: (5x - 2)*(5 - 3x) ≠ 0
5x - 2 = 0, 5x = 0, x = 2/5, x ≠ 0,4
5 - 3x = 0, -3x = - 5, x = 5/3, x ≠ 1(2/3)
Решим неравенство методом интервалов:
3 + 2x = 0, 2x = - 3, x = - 1,5
--(-∞)---( + )[-1.5]( - )(0,4)( + )---(12/3))( - )--(+∞)-->
x∈ [ -1,5;0,4)∪( 1(2/3);+∞)
