Question

Rezolvați inecuațiile:
@3(7x - 2) – 8(2x - 7) <0;
c)2(4x + 2) – 8(-4x + 1) <-14 - 15(-x+1);​

Answer 1

Răspuns:

3(7x - 2) – 8(2x - 7) < 0

21x - 6 - 16x + 56 < 0

5x + 50 < 0

5x < - 50

x < - 50 : 5

x < - 1`0

x ∈ ( - ∞; -10)

2(4x + 2) – 8(-4x + 1) <-14 - 15(-x+1)

8x + 4 + 32x - 8 < - 14 + 15x - 15

40x - 4 < 15x - 29

40x - 15x < - 29 + 4

25x < - 25

x < - 25 : 25

x < - 1

x ∈ ( - ∞; - 1 )

#copaceibrainly

Answer 2

Răspuns:

(a)  $\bf x\in( -\infty,-10)$

(c)  $\bf x\in (-\infty, -1)$

Explicație pas cu pas:

Salutare!

(a)

$\bf 3\cdot(7x - 2)- 8\cdot(2x - 7) < 0$

$\bf 21x - 6 - 16x +56 < 0$

$\bf 21x - 16x +50 < 0$

$\bf 5x +50 < 0$

$\bf 5x < -50\:\:\:\Big|:5$

$\bf x < -10 \implies\boxed{\bf x\in( -\infty,-10)}$

(c)

$\bf 2\cdot(4x + 2) - 8\cdot(-4x + 1) <-14 - 15\cdot(-x+1)$

$\bf 8x + 4 +32x -8 <-14 + 15x-15$

$\bf 40x -4 <-29 + 15x$

$\bf 40x -15x-4 <-29$

$\bf 25x-4 <-29$

$\bf 25x <-29 +4$

$\bf 25x <-25\:\:\:\Big|:25\:\:\:\text{\it(impartim toata relatia cu 25)}$

$\bf x <-1\implies \boxed{\bf x\in (-\infty, -1) }$

Regula de semnelor:

(+) · (+) = (+)

(+) · (-) = (-)

(-) · (-) = (+)

(-) · (+) = (-)

#copaceibrainly