Question

Rezolvati in R ecuatiile

Indrumat-va dupa poza si ajutati-ma, ofer coroana

Answer 1

a) [x]=1 atunci 1<=x<2  S=[1;2)

b)[x+3/2]=5

5<=x+3/2<6

3,5<=x<4,5 S=[3,5;4,5)

c) [x+1/2]+[x+5/2]=12

12<= x+1/2+x+5/2<13

9<=2x<10

S=[4,5;5)

d) [(2x+3)/5]=(x-1)/2

(x-1)/2<=(2x+3)/5<(x+1)/2          |    *10

5x-5<=4x+6<5x+5                    | -5x-6

-11<= -x< -1                                 | *(-1)

1 < x<=11

S=(1;11]

e) [(x-3)/2]=[(x-2)/3]

[(x-3)/2]-[(x-2)/3]=0

0<=(x-3)/2-(x-2)/3<1                  |*6

0<= 3x-9-2x+4<6

0<=x-5<6

5<= x <11

S=[5;11)

f) [(3x-7)/4] +[(3x-5)/4]= (5x+3)/7

(5x+3)/7<=(3x-7)/4 +(3x-5)/4 <(5x+10)/7       |*28

20x+12<=21x-49+21x-35<20x +40               |-20x+84

100<=22x<144 | *(1/2)

50<=11x<72

S=[50/11;72/11)

 Unde S este multimea solutiilor