Question

Giải phương trình sau: \(\dfrac{5x-1}{6}+\dfrac{2\left(x+4\right)}{9}=\dfrac{7x-5}{15}+x-1\)

Answer 1

\(\dfrac{5x-1}{6}+\dfrac{2\left(x+4\right)}{9}=\dfrac{7x-5}{15}+x-1\)

=>15(5x-1)+20(x+4)=6(7x-5)+90x-90

<=>\(75x-15+20x+80=42x-30+90x-90\)

<=>\(95x+65=132x-120< =>37x=185< =>x=5\)

vậy............

Answer 2

\(\dfrac{5x-1}{6}+\dfrac{2\left(x+4\right)}{9}=\dfrac{7x-5}{15}+x-1\)

\(\Leftrightarrow\dfrac{5}{6}x-\dfrac{1}{6}+\dfrac{2}{9}x+\dfrac{8}{9}=\dfrac{7}{15}x-\dfrac{5}{15}+x-1\)

\(\Leftrightarrow\left(\dfrac{5}{6}+\dfrac{2}{9}-\dfrac{7}{15}-1\right)x=-\dfrac{5}{15}-1+\dfrac{1}{6}-\dfrac{8}{9}\)

\(\Leftrightarrow\dfrac{-37}{90}x=\dfrac{-37}{18}\)

\(\Leftrightarrow x=\dfrac{-37}{18}:\dfrac{-37}{90}\)

\(\Leftrightarrow x=5\)

Answer 3

\(\dfrac{5x-1}{6}+\dfrac{2\left(x+4\right)}{9}=\dfrac{7x-5}{15}+x-1\)

\(\Leftrightarrow\dfrac{75x-15}{90}+\dfrac{20x+80}{90}=\dfrac{42x-30}{90}+\dfrac{90x}{90}-\dfrac{90}{90}\)

\(\Rightarrow75x-15+20x+80=42x-30+90x-90\)

\(\Leftrightarrow-37x=-55\Leftrightarrow x=\dfrac{55}{37}\)

Vậy S ={\(\dfrac{55}{37}\)}