Question

Rezolvati urmatoarele inecuatii folosind explicitarea in tabel:
3(x+1)-2|x+2|>x-3 ; 3x-1+3|1-x|≤2x+5

Answer 1

l) 3(x+1)-2|x+2|>x-3
3x+3-2|x+2|>x-3
-2|x+2|>x-3-3x-3
-2|x+2|>-2x-6
-2|x+2|>-2(x+3) /:(-2)
|x+2|>x+3
x+2<-(x+3) sau x+2>x+3
x+2<-x-3 sau x=∅
x+x<-3-2
2x<-5
x<-2½
x apartine (-∞;-2½)



ll) 3x-1+3|1-x|≤2x+5
3|1-x|≤2x+5-3x+1
3|1-x|≤-x+6
|1-x|≤(6-x)/3
1-x≤(6-x)/3 sau 1-x≥-(6-x)/3
6-x≤3(1-x) sau x+6≥3(1-x)
6-x≤3-3x sau x+6≥4-3x
-x+3x≤3-6 sau x+3x≥4-6
2x≤-3 sau 4x≥-2
x≤-1½ sau x≥-½
x apartine ∅