Question

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Answer 1

Răspuns:

a.{4lxl≥2=> lxl≥2/4  

lxl≥1/2=>

x≥-1/2   si x≥1/2=>

x∈(-∞,-1/2]U[[1/2,∞)

l3x-2l<4=>

-4<3x-2<4

-4+2<3x<4+2

-2<3x<6

-2/3<x<6/3=2

x∈(-2/3,2)

x∈(-∞,-1/2]U[1/2,+∞)∩(-2/3,2)=

(-2/3,-1/2]∪[1/2,2)

revin imediat  cu  b

b)(2x-7)/(x+2)<1

(2x-7)/(x+2)-1<0

[(2x-7)-(x+2)]/(x+2)<0

(2x-7-x-2)/(x+2)<0

(x-9)/(x+2)<0

Rezolvi  ecuatiile

x-9=0     x=9

si x+2=0  x= -2

Tabelul de  semne

x       l-∞                      -2         0                    9               +∞

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x-9  l----------------  --   --    -     -     -   -     -   -  0+     +    +  +

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x+2l  -∞----------------------0++++++++++++++++++++++++++++++++++

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x-9/(x+2)l+++++++++++++l-------------------------_0+++++++++++++++++++

Iei valoarea  cu  -

Deci  x∈(-2, 9]

l4x+1l≤5

-5≤4x+1≤5

-5-1≤4x≤5-1

-6≤4x≤4║:4

-6/4≤x≤4/4

-3/2≤x≤1

x∈[-3/2,1]

Intersectezi intervalele

X∈(-2,9]∩[-3/2.1]=[-3/2,1]

Explicație pas cu pas: