N1
log 7 (2 - x) =< log 7 (2x^2 - x)
2 - x =< 2x^2 - x
2x^2 - 2 >= 0
x € (-беск. ; -1] U [1 ; +беск.)
N2
log 0,5 (x^2 - 1) < -3
log 0,5 (x^2 - 1) < log 0,5 (8)
x^2 - 1 > 8
x^2 - 9 > 0
x € (-беск. ; -3) U (3 ; +беск.)
N3
lg (7^(6 - 2x) + 3) - lg (39) > lg (4) - lg (3)
lg (7^(6 - 2x) + 3) > lg (39) + lg (4) - lg (3)
lg (7^(6 - 2x) + 3) > lg (52)
7^(6x - 2) + 3 > 52
7^(6x - 2) > 49
6x - 2 > 2
6x > 4
x > 2/3
N4
log 2x + 1 (5 - 2x) > 1
log 2x + 1 (5 - 2x) > log 2x + 1 (2x + 1)
5 - 2x > 2x + 1
- 4x > - 4
x < 1
log 2x + 1 (5 - 2x) > 1
log 2x + 1 (5 - 2x) > log 2x + 1 (2x + 1)
5 - 2x < 2x + 1
-4x < -4
x > 1
2x + 1 > 0
x € (-1/2 ; 0)
5 - 2x > 0
x € (0 ; 5/2)
{x € (-1/2 ; 0) x - не существует
{x > 1
{x € (0 ; 5/2) x € (0 ; 1)
{x < 1
ответ : (0 ; 1
7-x=3+7x
7x+x=7-3
8x=4
x=0,5
2)9 - 2х/3 = 7+ х/3
9-2x=7+x
x+2x=9-7
3x=2
x=2/3
3)х+3/2 = х - 4
x+3=2x-8
2x-x=3+8
x=11
4)2 - 3х = х-12/2
4-6x=x-12
x+6x=4+12
7x=16
x=16/7=2 2/7