Question

3*[2|2x-5|-15]-12 mai mic sau egal 9,x€Z​

Answer 1

3*[ 2|2x - 5| - 15 ] - 12 ≤ 9

3*[ 2|2x - 5| - 15 ] ≤ 9+12

3*[ 2|2x - 5| - 15 ] ≤ 21

[ 2|2x - 5| - 15 ] ≤ 21/3

2|2x - 5| - 15 ≤ 7

2|2x - 5|  ≤7+15

2|2x - 5| ≤ 22

|2x - 5| ≤ 22/2

|2x - 5| ≤ 11  =>

-11 ≤ 2x - 5 ≤ 11 | (+5) =>

-6 ≤ 2x ≤ 16 | (:2)   =>

-3 ≤ x ≤8

x ∈ {-3;-2;-1;0;1;2;3;4;5;6;7;8}  => x este nr intreg , deci x apartine lui Z

Answer 2

Răspuns:

{-3,-2,-1,0,1,2,3,4,5,6,7,8}

Explicație pas cu pas:

3*[2|2x-5|-15]-12≤9

3*[2|2x-5|-15]≤9+12

3*[2|2x-5|-15]≤21

2|2x-5|-15≤21:3

2|2x-5|-15≤7

2|2x-5|≤7+15

2|2x-5|≤22

|2x-5|≤22:2

|2x-5|≤11

-11≤2x-5≤11, |+5

-11+5≤2x-5+5≤11+5

-6≤2x≤16, |:2

-3≤x≤8, deci x∈[-3; 8]∩Z={-3,-2,-1,0,1,2,3,4,5,6,7,8}