1. (x-3)(x+1)≥0
x=3 x=-1
+ - +
-------- -1 ----------- 3 ---------
\\\\\\\\\ \\\\\\\\\\\\
(3; +∞) х=4 + + | +
(-1; 3) х=0 - +| -
(-∞; -1) х=-2 - - | +
x∈(-∞; -1]U[3; +∞)
2.
x-3 <0<br> (x+1)(x-2)
{x+1≠0
{x-2≠0
{(x-3)(x+1)(x-2)<0<br>
{x≠-1
{x≠2
(x-3)(x+1)(x-2)<0<br>x=3 x=-1 x=2
- + - +
-------- -1 --------- 2 ------------ 3 -----------
\\\\\\\\ \\\\\\\\\\\\
(3; +∞) х=4 + + + | +
(2; 3) х=2,5 - + + | -
(-1; 2) х=0 - + - | +
(-∞; -1) х=-2 - - - | -
x∈(-∞; -1)U(2; 3)
3.
(x-1)(2-x)≥0
x+3
{x+3≠0
{(x-1)(2-x)(x+3)≥0
x≠-3
(x-1)(2-x)(x+3)≥0
-(x-1)(x-2)(x+3)≥0
(x-1)(x-2)(x+3)≤0
x=1 x=2 x=-3
- + - +
-------- -3 --------- 1 ------------ 2 --------------
\\\\\\\\\ \\\\\\\\\\\\
(2; +∞) х=3 + + + | +
(1; 2) х=2,5 + + - | -
(-3; 1) х=0 - - + | +
(-∞; -3) х=-4 - - - | -
x∈(-∞; -3)U [1; 2]