Question

11 Rezolvaţi în Z inecuațiile:
a 2(x - 1) < -6;
d 2(x + 8) S-10;
g 3 + 2(x + 2) < 5;
b 3(x + 1) < -18;
e 5(x - 1) < 0;
h 1+ 4(x - 1) <-7;
c 4(x + 2) 2-8;
f 2(x + 5) + 3 <-9;
i 5(2 + 3x) < -5. plis dau coroana​

Answer 1

Răspuns:

Explicație pas cu pas:

a)  2(x - 1) < -6 <=>

2x-2 < -6 => 2x < -6+2 => 2x < -4  I:2 =>

x < -2  I x ∈ Z

b) 3(x + 1) < -18   I : 3 =>

x + 1 < -6 => x < -1-6 =>

x < -7  I  x ∈ Z

c) 4(x + 2) < -8  I : 4  =>

x +2 < -2  => x < -2-2 =>

x < -4   I  x ∈ Z

d) 2(x + 8) < -10 I:2 =>

x+8 < -5 => x < -5-8 =>

x < -13  I  x ∈ Z

e) 5(x - 1) < 0 <=> 5x-5 < 0 => 5x < 5 I:5 =>

x < 1 I  x ∈ Z

f) 2(x + 5) + 3 < -9  <=>

2x+10 < -9-3 => 2x < -10-12 => 2x < -22 I:2 =>

x < -11 I  x ∈ Z

g) 3 + 2(x + 2) < 5 <=>

3+2x+4 < 5 => 2x < 5-3-4 => 2x < -6 =>

x < -3 I  x ∈ Z

h) 1+ 4(x - 1) < -7 <=>

1+4x-4 < -7 => 4x < -7-1+4 => 4x < -4  I:4 =>

x < -1  I x∈ Z

i) 5(2 + 3x) < -5  I:5 =>

2+3x < -1 => 3x < -1-2 => 3x < -3 I:3 =>

x < -1 I x∈ Z

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