Rozwiąż nierówność: a)2<|x|<4 b)-3<|x+5|≤7 c)0≤|x|<5 d)-2<2x-6|≤3 e)0<|x-2|<1 f)4≤|x-1|<6 Z obliczeniami!

a) 2 < I x I < 4 <=> I x I > 2 ∧ I x I < 4 <=> <=> x ∈ (-∞, -2) u ( 2,+∞) ∧ x ∈ (-4 ; 4) <=> <=> x ∈ (-4; -2) v x ∈ ( 2 ; 4) b) -3 < I x + 5 I ≤ 7 <=> x ∈ R ∧ I x +5 I ≤ 7 <=> <=> x∈ R ∧ ( x+5 ≤ 7 ∧ x+5 ≥ -7 ) <=> <=> x ∈ R ∧ ( x ≤ 7 - 5 = 2 ∧ x ≥ - 7 - 5 = -12 ) <=> <=> x ∈ < -12 ; 2 > c) 0 ≤ I x I < 5 <=> x ∈ R ∧ I x I < 5 <=> <=> x ∈ R ∧ ( -5 < x < 5 ) < => x ∈ ( -5 ; 5) d) -2< I 2x - 6 I ≤ 3 < => x ∈ R ∧ ( -3 ≤ 2x - 6 ≤ 3 ) <=> <=> x ∈ R ∧ ( 2x - 6 ≥ -3 ∧ 2x ≤ 3 +6 ) <=> <=> x ∈ R ∧ ( 2x ≥ -3 + 6 = 3 ∧ 2x ≤ 9 ) <=> <=> x ∈ R ∧ ( x ≥ 1,5 ∧ x ≤ 4,5 ) <=> x ∈ < 1,5 ; 4,5 > e) 0 < I x - 2 I < 1 <=> x ∈ R {2} ∧ I x - 2 I < 1 <=> <=> x ∈ R { 2 } ∧ ( -1 < x -2 < 1 ) <=> <=> x ∈ R { 2 } ∧ ( x - 2 > -1 ∧ x -2 < 1 ) <=. <=> x ∈ R { 2 } ∧ ( x > -1 +2 = 1 ∧ x < 1 +2 = 3 ) <=> <=> x ∈ R {2 } ∧ x ∈ (1 ; 3) <=> x ∈ (1 ;2) u (2; 3) f) 4 ≤ I x - 1 I < 6 <=> I x - 1 I ≥ 4 ∧ I x - 1 I < 6 <=> <=> ( - 4 ≥ x - 1 ≥ 4 ) ∧ ( -6 < x - 1 < 6 ) <=> <=> ( x-1 ≤ -4 ∨ x -1 ≥ 4 ) ∧ ( x-1 >-6 ∧ x - 1 < 6 ) <=> <=> ( x ≤ -4 +1 = -3 ∨ x ≥ 4+1 = 5 ) ∧ (x > -5 ∧ x < 7 ) <=> <=> ( x ≤ -3 ∨ x ≥ 5 ) ∧ x ∈ ( -5 ; 7) <=> <=> x∈ (-5; -3 > u < 5; 7)

Rozwiąż nierówność: a)2<|x|<4 |x|<4 i 2<|x| -4 c)0≤|x|<5 |x|<5 i 0≤|x| -5 e)0<|x-2|<1 |x-2|<1 i 0<|x-2| -1u<5;7)