Question

Rezolvati în mulțimea nr raționale, ecuația
2x+1/3=×-3/6-×+3/4+2×+1/12​

Answer 1

Explicație pas cu pas:

2x+1/3=x-3/6- x+3/4+2x+1/12

amplificam prima fractie cu 4, a doua cu 2 si ultima ramane asa

si avem:

(2x+1)×4 /12=(x-3)×2+2x+1 /12

8x+4/12= 2x+6+2x+1 / 12

8x+4/12= 4x+7/12

(8x+4)×12= (4x+7)×12

96x+48=48x+84

96x-48x=84-48

48x=36

x=36/48 simplificam cu12

x=3/4

Answer 2

$\frac{2x+1}{3}=\frac{x-3}{6}-\frac{x+3}{4}+\frac{2x+1}{12}=\frac{2(x-3)}{12}-\frac{3(x+3)}{12}+\frac{2x+1}{12} \\ \Rightarrow \frac{2x+1}{3}=\frac{2x-6-3x-9+2x+1}{12}=\frac{x-14}{12} \\ \Rightarrow2x+1=\frac{x-14}{4} \ \Leftrightarrow \ x-14=4(2x+1)=8x+4 \\ \Rightarrow x=14+8x+4=18+8x \ \Leftrightarrow 18=x-8x=-7x \\ \Rightarrow \boxed{x=-\frac{18}{7}}$