Question

[Cô Bảo Bình]

\(\dfrac{5+x}{4-x}=\dfrac{1}{2}\)

\(\dfrac{25}{14}=\dfrac{x+7}{x-4}\)

\(\dfrac{3x-5}{x+4}=\dfrac{5}{2}\)

\(\dfrac{3x-1}{2x+1}=\dfrac{3}{7}\)

Answer 1

[An Nguyễn Bá]

a) \(\dfrac{5+x}{4-x}=\dfrac{1}{2}\)

\(\Leftrightarrow2\left(5+x\right)=4-x\)

\(\Leftrightarrow2\left(5+x\right)-\left(4-x\right)=0\)

\(\Leftrightarrow10+2x-4+x=0\)

\(\Leftrightarrow6+3x=0\)

\(\Leftrightarrow3x=-6\)

\(\Leftrightarrow x=-2\)

Vậy x=-2

b) \(\dfrac{25}{14}=\dfrac{x+7}{x-4}\)

\(\Leftrightarrow25\left(x-4\right)=14\left(x+7\right)\)

\(\Leftrightarrow25\left(x-4\right)-14\left(x+7\right)=0\)

\(\Leftrightarrow25x-100-14x-98=0\)

\(\Leftrightarrow11x-198=0\)

\(\Leftrightarrow11x=198\)

\(\Leftrightarrow x=18\)

Vậy x=18

c) \(\dfrac{3x-5}{x+4}=\dfrac{5}{2}\)

\(\Leftrightarrow2\left(3x-5\right)=5\left(x+4\right)\)

\(\Leftrightarrow2\left(3x-5\right)-5\left(x+4\right)=0\)

\(\Leftrightarrow6x-10-5x-20=0\)

\(\Leftrightarrow x-30=0\)

\(\Leftrightarrow x=30\)

Vậy x=30

d) \(\dfrac{3x-1}{2x+1}=\dfrac{3}{7}\)

\(\Leftrightarrow7\left(3x-1\right)=3\left(2x+1\right)\)

\(\Leftrightarrow7\left(3x-1\right)-3\left(2x+1\right)=0\)

\(\Leftrightarrow21x-7-6x-3=0\)

\(\Leftrightarrow15x-10=0\)

\(\Leftrightarrow15x=10\)

\(\Leftrightarrow x=\dfrac{10}{15}=\dfrac{2}{3}\)

Vậy \(x=\dfrac{2}{3}\)