7.
(3x-1)² (2x+3)(5-x) ≥0
x(x-1)
x≠0
x≠1
x(x-1)(3x-1)(3x-1)(2x+3)(5-x)≥0
-x(x-1)*3(x-¹/₃)*3(x-¹/₃)*2(x+1.5)(x-5)≥0
x(x-1)(x-¹/₃)(x-¹/₃)(x+1.5)(x-5)≤0
x=0 x=1 x=¹/₃ x= -1.5 x=5
+ - + + - +
----- -1.5 ---------- 0 ------------ 1/3 ---------- 1 ------- 5 ------------
\\\\\\\\\ \\\\\\\\\\
x=6 + + + + + + | +
x=4 + + + + - + | -
x=0.5 + - - + - - | +
x=0.1 + - - + - - | +
x=-1 - - - + - - | -
x= -2 - - - - - - | +
x∈{1/3} U [-1.5; 0) U (1; 5]
10.
2x-11 + 19-2x < 2x
4 2
2x-11 +2(19-2x)-8x<0<br>2x-11+38-4x-8x<0<br>-10x<-27<br>x>2.7
2x+1.5 > 1/5 (x-1) +(x/3)
9
2x+1.5 > 9.*0.2(x-1)+3x
2x+1.5 >1.8x-1.8+3x
-2.8x>-3.3
x<33/28<br>x<1 ⁵/₂₈<br>
1⁵/₂₈ x=2 - целое число, удовлетворяющее системе.
Ответ: 2.