Question

Rezolvati, in multimea numerelor naturale, inecuatiile:

a) 7x - 5 mai mic sau egal 2x + 60

b) 18x + 256 > 7 • (2x + 103)

c) 12x + 9 mai mic sau egal 4(3x + 2)

d) x + 9x < 73 + 37

e) 2 • [ 10 + 7 • (82 - 9 la puterea 2)] + x < 2011

f) 41 la puterea x + 6 < 41 la puterea 10

Va rog ajutati-ma!!!
Dau coronita!

Answer 1

a) 7x-5<=2x+60. nu pot pune mai mic sau egal si il scriu <=
7x-2x=60+5
5x<=65
x<=65:5
x<=13
S={0,1,2,3,4,5,6,7,8,9,10,11,12,13}


b) 18x+256>7•(2x+103). sau. 18x-14x>721-256. altfel nu am stiut
18x+256>14x+721. 32x>465
18x+14x>721-256. x>465:32
| 4x>465. | x>14 r17
| x>465:4 |
| x>116 r1. |


c) 12x<=4(3x+2)
12x<=12x+8
12x+12x<=8
24x<=8
x<=24:8
x<=3
S={0,1,2,3}


d) x+9x<73+37
10x<110
x<110:10
x<11
S={0,1,2,3,4,5,6,7,8,9,10}


e) 2•[10+7•(82-9^2)]+x<2011. nu pot sa scriu la putere si scriu asa ^
2•[10+7(82-81)]+x<2011
2•(10+7•1)+x<2011
2•(10+7)+x<2011
20+14+x<2011
x<2011+20-14
x<2017
S={0,1,2,...,2017



f) 41^x+6<41^10
41(x+10)<6
41x+410<6
41x<410-6
41x<404
x<404:41
x<9 r35