Question

Ex 1 și 3 dau coroana e urgentttttt. multumesc!

Answer 1

Explicație pas cu pas:

1.

a) x ∈ (3; +∞)

$x - 3 > 0 = > x > 3$

b) x ∈ (-∞ ;4]

$- x + 4 \geqslant 0 < = > - x \geqslant - 4 = > x \leqslant 4$

c) x ∈ (-∞ ; -4)

$x + 4 < 0 = > x < - 4$

d) x ∈ (1; +∞)

$x - 2 > - 1 < = > x > - 1 + 2 = > x > 1$

e) x ∈ (-∞ ; -3)

$2x + 6 < 0 < = > 2x < - 6 |÷2= > x < - 3$

f) x ∈ (-∞ ; -4)

$x + 3 < - 1 < = > x < - 1 - 3 = > x < - 4$

g) x ∈ (4; +∞)

$3x-12>0 < = > 3x > 12|÷3 = > x > 4$

h) x ∈ (-∞ ; 1)

$2x + 5 < 7 < = > 2x < 2|÷2 = > x < 1$

3.

a) x ∈ (-∞ ; 2]

$2(4x - 1) \leqslant 14 \\ 8x - 2 \leqslant 14 \\ 8x \leqslant 16|÷8 = > x \leqslant 2$

b) x ∈ [4; +∞)

$5(4x - 6) \geqslant 50 \\ 20x - 30 \geqslant 50 \\ 20x \geqslant 80÷|20 = > x \geqslant 4$

c) x ∈ (-∞ ; 2]

$6(3x - 4) \leqslant 6x \\ 18x - 24 \leqslant 6x \\ 12x \leqslant 24|÷12 = > x \leqslant 2$

d) x ∈ (3; +∞)

$3(5x + 2) > 21 \\ 15x + 6 > 21 \\ 15x > 15|÷15 = > x > 3$

e) x ∈ (-∞ ; -3)

$10(x - 3) - 3(x - 3) < - 42 \\ 10x - 30 - 3x + 9 < - 42 \\ 7x < - 42 + 21 \\ 7x < - 21|÷7 = > x < - 3$

f) x ∈ (-4; +∞)

$6(x - 6) - 5(x + 4) > - 60 \\ 6x - 36 - 5x - 20 > - 60 \\ x > - 60 + 56 \\ x > - 4$