Question

Determinati numerele naturale care verifica inegalitatile:
a.3(x-2)< sau egal 3
b.4x+7<23
c.3x+7-2x<10
d.182-153>sau egal x+19
e.2x+10<20
f.5x+7<4x+9
VA ROG E URGEEEENT!!!

Answer 1

$a)3(x - 2) \leqslant 3$

$3x - 6 \leqslant 3$

$3x \leqslant 3 + 6$

$3x \leqslant 9 \: | \div 3$

$x \leqslant 3$

$x \: \in \: \mathbb{N} = > x \: \in \: \left\{0,1,2,3\right\}$

$b)4x + 7 < 23$

$4x < 23 - 7$

$4x < 16 \: | \div 4$

$x < 4$

$x \: \in \: \mathbb{N} = > x \: \in \: \left\{0,1,2,3\right\}$

$c)3x + 7 - 2x < 10$

$3x - 2x < 10 - 7$

$x < 3$

$x \: \in \: \mathbb{N} = > x \: \in \: \left\{0,1,2\right\}$

$d)182 - 153 \geqslant x + 19$

$29 \geqslant x + 19$

$- x \geqslant 19 - 29$

$- x > - 10 \: | \times ( - 1)$

$x < 10$

$x \: \in \: \mathbb{N} = > x \: \in \: \left\{0,1,2,3,4,5,6,7,8,9\right\}$

$e)2x + 10 < 20$

$2x < 20 - 10$

$2x < 10 \: | \div 2$

$x < 5$

$x \: \in \: \mathbb{N} = > x \: \in \: \left\{0,1,2,3,4\right\}$

$f)5x + 7 < 4x + 9$

$5x - 4x < 9 - 7$

$x < 2$

$x \: \in \: \mathbb{N} = > x \: \in \: \left\{0,1\right\}$