Question

determinati x nr nat din;  
a. 2(x-2)<sau =10 
b. (x+4) *6-24<= 12 
c. 144:(x-5)>9 si x:7 >2 
d. 3x <=27 si 4x >=12 
e. [(x-144:12) *3-2]:7<=4 
f. 2<=x <=10 si 3x-4>=23 

Answer 1

a) $2(x-2) \leq 10 |:2$
$x-2 \leq 5$
$x \leq 5+2$
$x \leq 7$

b)$(x+4)*6-24 \leq 12 |:6$
$(x+4)-4 \leq 2$
$x \leq 2$

c) $144:(x-5)>9$
$9(x-5)>144$
$x-5> \frac{144}{9}$
$x-5>16$
$x>16+5$
$x>21$

$x:7>2$
$x>2*7$
$x>14$

d)$3x \leq 27$
$x \leq \frac{27}{3}$
$x \leq 9$

$4x \geq 12$
$x \geq \frac{12}{4}$
$x \geq 3$

e)$[(x-144:12)*3-2]:7 \leq 4$
$(x-12)*3-2 \leq 4*7$
$(x-12)*3-2 \leq 28$
$(x-12)*3 \leq28+2$
$(x-12)*3 \leq30$
$x-12 \leq \frac{30}{3}$
$x-12 \leq 10$
$x \leq 10+12$
$x \leq 22$

f)$2 \leq x \leq 10 |:2$
$1 \leq x \leq 5$
x∈{1; 2; 3; 4; 5}

$3x-4 \geq 23$
$3x\geq 23+4$
$3x \geq 27$
$x \geq \frac{27}{3}$
$x \geq 9$