Question

Giai phuong trinh :\(\frac{x-3}{11}+\frac{x+1}{3}=\frac{x+7}{9}-1\)

Answer 1

\(\frac{x-3}{11}+\frac{x+1}{3}=\frac{x+7}{9}-1\)

\(\Leftrightarrow\frac{9\left(x-3\right)}{99}+\frac{33\left(x+1\right)}{99}=\frac{11\left(x+7\right)}{99}-\frac{99}{99}\)

\(\Leftrightarrow\frac{9\left(x-3\right)+33\left(x+1\right)}{99}=\frac{11\left(x+7\right)-99}{99}\)

\(\Leftrightarrow9\left(x-3\right)+33\left(x+1\right)=11\left(x+7\right)-99\)

\(\Leftrightarrow9x-27+33x+33=11x+77-99\)

\(\Leftrightarrow42x+6=11x-22\Leftrightarrow42x-11x=-6-22\)

\(\Leftrightarrow31x=-28\Leftrightarrow x=-\frac{28}{31}\)

Vậy phương trình có tập nghiệm S={-28/31}