Question

Numerele intregi care verifica ecuatia l 2x - 3 l = 5 calculat este : 

Answer 1

|2x-3|=5 este echivaleta cu:

$2x-3=\pm5$

2x+3=5⇒x=1
2x+3=-5⇒x=-4

Deci x∈{1; -4}

Answer 2

l 2x - 3 l = 5

l 2x - 3 l = 2x - 3  daca  2x - 3 > 0  => x > 3/2

l 2x - 3 l = -(2x - 3)  daca  2x - 3 < 0  => x < 3/2

Avem ecuatiile:
1)  
 2x - 3 = 5  
2x = 5 + 3  
2x = 8  
x = 8 / 2 = 4

2)   
-(2x - 3) = 5
-2x + 3 = 5
-2x = 5 - 3
-2x = -2 
x = (-2) / (-2) = -1

PROBE:
1)
x = 4
l 2*4 - 3 l =l 8 - 3 l = l 5 l = 5   OK

2)
x = -1
l 2*(-1) - 3 l = l -2 - 3 l = l -5 l = 5  OK