Question

20. Determinați numerele negative mai mari ca (-5) care verifică inegalităţile: a) x + 2 ≤3; b) 3x - 1 ≤ 5; c) x + 1 ≥-3; d) -3x+2> 2r - 8; e) | x | ≤ 2; f) |x-1|≤2. 25. L se imp​

Answer 1

Răspuns:

numerele negative mai mari ca (-5)

Explicație pas cu pas:

a)

$x + 2 \leqslant 3 |_{- 2} \iff x \leqslant 1 \\ \implies x\in \{-4; -3; -2; -1\}$

b)

$3x - 1 \leqslant 5 |_{+ 1}\iff 3x \leqslant 6 |_{: 3}\\ x \leqslant 2 \implies x\in \{-4; -3; -2; -1\}$

c)

$x + 1 \geqslant - 3 |_{- 1}\iff x \geqslant - 4 \\ \implies x\in \{-4; -3; -2; -1\}$

d)

$- 3x + 2 > 2x - 8 \iff - 3x - 2x > - 8 - 2 \\ - 5x > - 10 |_{ \cdot (- 1)}\iff 5x < 10 |_{: 5}\\ x < 2 \implies x\in \{-4; -3; -2; -1\}$

e)

$|x| \leqslant 2 \iff - 2 \leqslant x \leqslant 2 \\ \implies x\in \{-2; -1\}$

f)

$|x - 1| \leqslant 2 \iff - 2 \leqslant x - 1 \leqslant 2 |_{+ 1}\\- 1 \leqslant x \leqslant 3 \implies x\in \{-1\}$