Question

x este solutie a ecuatiei : (2x+1)+(2x + 2) +........+ (2x+100) = 5650

Answer 1

$(2x+1)+(2x+2)+...+(2x+100)=5650 \\ (2x+2x+...2x)+(1+2+...+100)=5650 \\ 100*2x+ \frac{100*101}{2}=5650 \\ 200x+5050=5650 \\ 200x=600 \\ \boxed{x=3}$

Answer 2

Daca desfacem parantezele, avem 2x+1+2x+2+...+2x+100=5650
2x*100+(1+2+3+...+100)=5650
200x+100*101/2=5650
200x+5050=5650
200x=600
x=3