Question

Giải Phương trình 
\(x-\dfrac{x+2}{3}< 3x+\dfrac{x}{2}+5 \)
\(\dfrac{x}{2}+\dfrac{1-x}{3}>0\)
\(\left(x-9\right)^2-x\left(x+9\right)< 0\)

Answer 1

a. \(x-\dfrac{x+2}{3}< 3x+\dfrac{x}{2}+5\)

\(\Leftrightarrow\dfrac{6x}{6}-\dfrac{2\left(x+2\right)}{6}< \dfrac{18x}{6}+\dfrac{3x}{6}+\dfrac{30}{6}\)

\(\Rightarrow6x-2x-4-18x-3x-30< 0\)

\(\Leftrightarrow-17x< 34\)

\(\Leftrightarrow x>-2\)

b. \(\dfrac{x}{2}+\dfrac{1-x}{3}>0\)

\(\Leftrightarrow3x+2-2x>0\)

\(\Leftrightarrow x>-2\)

c. \(\left(x-9\right)^2-x\left(x+9\right)< 0\)

\(\Leftrightarrow x^2-18x+81-x^2-9x< 0\)

\(\Leftrightarrow-27x< -81\)

\(\Leftrightarrow x>3\)