Question

Determinati A reunit cu B, a intersectat cu B, A\b,B\a​

Answer 1

Răspuns:

a)

Multimea A :

|2x + 7| ≥ 15

-15 ≥ 2x + 7 ≥ 15    / -7

-22 ≥ 2x ≥ 8      / :2

-11 ≥ x ≥ 4

x ∈ [-11 ; 4]

Multimea B :

|2x-5| > 9

-9 > 2x-5 > 9     / +5

-4 > 2x > 14      / :2

-2 > x > 7

x ∈ (-2 ; 7)

A ∪ B = [-11 ; 7)

A ∩ B = (-2 ; 4]

A \ B = [-11 ; -3)

B \ A = (5 ; 7)

b)

Multimea A :

|2x+1| > 7

-7 > 2x + 1 > 7         / -1

-8 > 2x > 6        / :2

-4 > x > 3

x ∈ (-4 ; 3)

Multimea B :

|2x+3| ≥ 11

-11 ≥2x+3 ≥ 11      / -3

-14 ≥ 2x ≥ 8      / :2

-7 ≥ x ≥ 4

x ∈ [-7 ; 4]

A ∪ B = [-7 ; 4]

A ∩ B = (-4 ; 3)

A \ B = Ø

B \ A = [-7 ; - 5]

c)

Multimea A :

|2x-3| > 15

-15 > 2x-3 > 15       / +3

-12 > 2x > 18      /  :2

-6 > x > 9

x ∈ (-6 ; 9)

Multimea B :

|2x+7| > 19

-19 > 2x+7 > 19     / -7

-26 > 2x > 12     / :2

-13 > x > 6

x ∈ (-13 ; 6)

A ∪ B = (-13 ; 9)

A ∩ B = (-6 ; 6)

A \ B = (7 ; 9)

B \ A = (-13 ; -7)

Spor la teme!