Question

Exercitiul 1 va rog dau coroana

Answer 1

Răspuns:

a)5×+7<=3×+11

5x-3×+17<=11

2×+7<=11

2×<=11-7

2×<=4

×<=2

b)6×+11>=4(×+2)+13

6×+11>=4×+8+13

6×-4×+11>=21

2×+11>=21-11

2×>=10

×>=5

d)3/2×-1/+5×<5(×+5)+2

6×-3+5×<5×+25+2

11×-3<5×+27

11×-5×<27+3

6×<30

×<=5

Explicație pas cu pas:

Answer 2

Explicație pas cu pas:

a)

$5x + 7 \leqslant 3x + 11 \\ 5x - 3x \leqslant 11 - 7$

$2x \leqslant 4 \implies x \leqslant 2$

$x \in \Big\{1; 2\Big\}$

b)

$6x + 11 \geqslant 4(x + 2) + 13$

$6x + 11 \geqslant 4x + 8 + 13$

$6x - 4x \geqslant 21 - 11$

$2x \geqslant 10 \implies x \geqslant 5$

$x \in \Big[5 ; +\infty \Big)$

c)

$8x - 7 \geqslant 5x - 19 \\ 8x - 5x \geqslant - 19 + 7$

$3x \geqslant - 12 \implies x \geqslant - 4$

$x \in \Big\{-4; -3; -2; -1\Big\}$

d)

$x \geqslant 1 \iff 2x \geqslant 2 \implies 2x - 1 \geqslant 1 \\ \iff |2x - 1| = 2x - 1$

$3 |2x - 1| + 5x \leqslant 5(x + 5) + 2$

$3 (2x - 1) + 5x \leqslant 5x + 25 + 2$

$6x - 3 + 5x \leqslant 5x + 27$

$11x - 5x \leqslant 27 + 3$

$6x \leqslant 30 \implies x \leqslant 5$

$x \in \Big\{ 1; 2; 3; 4; 5 \Big\}$