Question

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Answer 1

Răspuns:

Explicație pas cu pas:

a)

2[3|2x - 3| -8 ] -9 ≤ 5

2[3|2x - 3| -8 ] ≤ 5 + 9

2[3|2x - 3| -8 ] ≤ 14

3|2x - 3| -8 ≤ 7

3|2x - 3| ≤ 7 + 8

3|2x - 3| ≤ 15

|2x - 3| ≤ 5 ⇔ -5 ≤ 2x-3 ≤ 5

-5 ≤ 2x-3 ≤ 5

-5+3 ≤ 2x-3+3 ≤ 5 +3

-2 ≤ 2x ≤ 8

-1 ≤ x ≤ 4

x∈[-1,4]

x∈ Z ⇒ x∈{-1, 0, 1, 2, 3, 4}

b)

29-3|2x - 7| ≥ -4

29+4 ≥ 3|2x - 7|

33 ≥ 3|2x - 7|

11 ≥ |2x - 7|

|2x - 7| ≤ 11 ⇔ -11 ≤ 2x -7 ≤ 11

-11 ≤ 2x -7 ≤ 11

-11 + 7 ≤ 2x - 7 + 7 ≤ 11 +7

-4 ≤ 2x ≤ 18

-2 ≤ x ≤ 9

x∈[-2 , 9]

x∈ Z* ⇒ x∈{-2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9}

c)

4(3x + 8) + 6|2x + 3| + 5 < 5(2x - 3) + 2x +94

12x + 32 + 6|2x + 3| + 5 < 10x - 15 + 2x +94

12x + 37 + 6|2x + 3| < 12x +79

6|2x + 3| < 42

|2x + 3| < 7 ⇔-7 < 2x + 3<7

-7 < 2x + 3<7

-7 - 3 < 2x + 3 - 3 <7 -3

-10 < 2x <4

-5 < x < 2

x∈(-5,2)

x∈Z ⇒ x∈{-4, -3, -2, -1, 0, 1}