Question

Giải các phương trình :

a) \(\dfrac{x}{3}-\dfrac{2x+1}{2}=\dfrac{x}{6}-x\)

b) \(\dfrac{2+x}{5}-0,5x=\dfrac{1-2x}{4}+0,25\)

Answer 1

a) \(\dfrac{x}{3}-\dfrac{2x+1}{2}=\dfrac{x}{6}-x\)

\(\Leftrightarrow\dfrac{2x}{6}-\dfrac{3\left(2x+1\right)}{6}=\dfrac{x}{6}=\dfrac{6x}{6}\)

\(\Leftrightarrow2x-3\left(2x+1\right)=x-6x\)

\(\Leftrightarrow2x-6x-3=x-6x\)

\(\Leftrightarrow2x-6x-x+6x=3\)

\(\Leftrightarrow x=3\)

\(S=\left\{3\right\}\)

b) \(\dfrac{2+x}{5}-0,5x=\dfrac{1-2x}{4}+0,25\)

\(\Leftrightarrow\dfrac{4\left(2+x\right)}{20}-\dfrac{10x}{20}=\dfrac{5\left(1-2x\right)}{20}+\dfrac{5}{20}\)

\(\Leftrightarrow4\left(2+x\right)-10x=5\left(1-2x\right)+5\)

\(\Leftrightarrow8+4x-10x=5-10x+5\)

\(\Leftrightarrow4x-10x+10x=5+5-8\)

\(\Leftrightarrow4x=2\)

\(\Leftrightarrow x=\dfrac{1}{2}\)

\(S=\left\{\dfrac{1}{2}\right\}\)

Answer 2

a)X= 3

b)X= 0,5

Answer 3