Question

1, Tìm x, biết

a, (2x+3).(3x-5) \(\ge\) 0

b, \(\dfrac{x}{3-x}\) > -1

c, \(\dfrac{3}{2}\) \(\le\) \(\dfrac{x-1}{x+5}\)

d, \(\dfrac{7}{4x^2-1}\) \(\ge\) 0

e, \(\dfrac{7}{x^2-3}\) > 1

Answer 1

a: \(\left(2x+3\right)\left(3x-5\right)\ge0\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-5\ge0\\2x+3\le0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>=\dfrac{5}{3}\\x< =-\dfrac{3}{2}\end{matrix}\right.\)

b: \(\dfrac{x}{3-x}>-1\)

\(\Leftrightarrow\dfrac{x}{3-x}+1>0\)

\(\Leftrightarrow\dfrac{x+3-x}{3-x}>0\)

=>3-x>0

hay x<3

c: \(\dfrac{x-1}{x+5}\ge\dfrac{3}{2}\)

\(\Leftrightarrow\dfrac{x-1}{x+5}-\dfrac{3}{2}\ge0\)

\(\Leftrightarrow\dfrac{2x-2-3x-15}{2\left(x+5\right)}>=0\)

\(\Leftrightarrow\dfrac{x+17}{2\left(x+5\right)}< =0\)

=>-17<=x<-5

d: \(\dfrac{7}{4x^2-1}\ge0\)

=>4x²-1>0

=>(2x-1)(2x+1)>0

=>x>1/2 hoặc x<-1/2