1.
ответ: 19 (решение по действиям):
1) 27,54 * 11/36 = 2754/100 * 11/36 = 153*11/100*2 = 8 83/200 (или 8,415),
2) 8,415 - 3,405 = 5,01,
3) 5,01 : 0,3 = 16,7,
4) 16 5/9 - 15 7/12 = (16-15) + (5/9-7/12) = 1 + (20/36-21/36) =
= 1 - 1/36 = 35/36,
5) 35/36 : 19 4/9 = 35/36 : 175/9 = 35/36 * 9/175 = 1/4*5 = 1/20 (или 0,05),
6) 0,05 + 3,18 = 3,23,
7) 7,429 : 3,23 = 2,3,
8) 16,7 + 2,3 = 19,
2.
11/(х-4) - 14х²/(х²-16) = 49/(х+4),
11*(х+4) - 14х² = 49*(х-4),
11х + 44 - 14х² = 49х - 196,
11х + 44 - 14х² - 49х + 196 = 0,
-14х² - 38х + 240 = 0,
7х² + 19х - 120 = 0,
Д = 19² - 4*7*(-120) = 361 + 3360 = 3721,
х1 = (-19+61)/2*7 = 42/14 = 3,
х2 = (-19-61)/7*2 = 80/14 = 5 5/7,
(х+1)/2 + (х+2)/3 = 17 - (3х-17)/4,
6*(х+1) + 4*(х+2) = 17*12 - 3*(3х-17),
6х+6 + 4х+8 = 204 - 9х + 51,
6х + 4х + 9х = 204 + 51 - 6 - 8,
19х = 241,
х = 12 13/19,
3.
х - (х-1)/3 - (2х-5)/5 < 7 - (х+8)/6,
30х - 10(х-1) - 6(2х-5) < 7*30 - 5(х+8),
30х - 10х + 10 - 12х + 30 < 210 - 5х - 40,
30х - 10х - 12х + 5х < 210 - 40 - 10 - 30,
13х < 130,
х < 10,
-3 ≤ 7х+4 ≤ 3,
7х+4 ≤ 3,
7х ≤ 3-4,
7х ≤ -1,
х ≤ -1/7,
7х+4 ≥ -3,
7х ≥ -3-4,
7х ≥ -7,
х ≥ -1, ⇒ ⇒ х ∈ (-1; -1/7)