1) (x-7)(x+10) < 0
x=7 x=-10
+ - +
-------- -10 -------- 7 ------------
\\\\\\\\\\
x∈(-10; 7)
2) 3x²+2x-1>0
3x²+2x-1=0
D=4+4*3*1=4+12=16
x₁=-2-4= -1
6
x₂=-2+4 = 1/3
6
+ - +
--------- -1 ------- 1/3 --------------
\\\\\\\\\ \\\\\\\\\\\\\\
x∈(-∞; -1) U (1/3; +∞)
3) x² -144 ≤0
(x-12)(x+12)≤0
x=12 x=-12
+ - +
--------- -12 ----------- 12 --------------
\\\\\\\\\\\\\\\
x∈[-12; 12]
4) x² +24x>0
x(x+24)>0
x=0 x=-24
+ - +
------------ -24 --------------- 0 --------------
\\\\\\\\\\\\ \\\\\\\\\\\\\
x∈(-∞; -24) U (0; +∞)
5) 7-x ≤0
x-10
{x-10≠0
{(7-x)(x-10)≤0
x≠10
(7-x)(x-10)≤0
-(x-7)(x-10)≤0
(x-7)(x-10)≥0
x=7 x=10
+ - +
--------- 7 ----------- 10 -------------
\\\\\\\\ \\\\\\\\\\\\\\\
x∈(-∞; 7] U (10; +∞)
6) x² + 11<0<br>нет решений, так как при любом Х неравенство всегда ≥ 0
7) 16x² -8x+1 ≤0
(4x-1)² ≤ 0
4x-1=0
4x=1
x=1/4
Здесь неравенство имеет только одно решение х=1/4
х∈{1/4}