Question

ex 9 ..............​

Answer 1

a) -2 < -4x+3 < 2 (scazi 3)

-5 < -4x < -1 (inmultesti cu -1 si schimbi semnul)

5 > 4x > 1 (imparti la 4)

$\frac{5}{4}$ > x > $\frac{1}{4}$

x ∈ ($\frac{1}{4}$, $\frac{5}{4}$)

b) -3 ≤ -3x-5 ≤ 3 (adaugi 5)

2 ≤ -3x ≤ 8 (imparti la -3, schimbi semnul)

$-\frac{2}{3}$ ≥ x ≥ $-\frac{8}{3}$

x ∈ ($-\frac{8}{3}$, $-\frac{2}{3}$)

c) -$\sqrt{2}$ |0,5x-0,2| ≥ $-\frac{\sqrt{18} }{10}$ (impartim la -$\sqrt{2}$, se schimba semnul)

|0,5x-0,2| ≤ $\frac{\sqrt{9} }{10}$

$-\frac{\sqrt{9} }{10}$ ≤ 0,5x-0,2 ≤ $\frac{\sqrt{9} }{10}$

$-\frac{3}{10}$≤ 0,5x-0,2 ≤ $\frac{3}{10}$ (aducem la acelasi numitor)

$-\frac{3}{10}$≤ $\frac{5x}{10} - \frac{2}{10}$ ≤ $\frac{3}{10}$

-3 ≤ 5x -2 ≤ 3 (adaugam 2)

-1 ≤ 5x ≤ 5

$-\frac{1}{5}$ ≤ x ≤ 1

x ∈ [$-\frac{1}{5}$ , 1]

d) Daca un modul este ≤ 0 asta inseamna ca acel modul este egal cu 0.

x $-\frac{3x+2}{5}$ = 0

x = $\frac{3x+2}{5}$ (aducem la acelasi numitor)

5x = 3x+2

2x = 2

x = 1

e) Nu imi dau seama cum un modul ar putea fi mai mic ca 0.

f) $-1 < 5-\frac{x+6}{2} < 1$ (scadem 5)

$-6 < -\frac{x+6}{2} < -4$ (inmultim cu -1, se schimba semnul)

$6 > \frac{x+6}{2} > 4$ (inmultim cu 2)

12 > x+6 > 8 (scadem 6)

6 > x > 2

x ∈ (2, 6)