ĐKXĐ x<>0

Ta có: \(\frac{2x+1}{x}+3\ge\frac{3-5x}{5}+\frac{4x+1}{4}\)

=>\(\frac{2x+1+3x}{x}\ge\frac{4\left(3-5x\right)+5\left(4x+1\right)}{20}=\frac{17}{20}\)

=>\(\frac{5x+1}{x}\ge\frac{17}{20}\)

=>\(\frac{5x+1}{x}-\frac{17}{20}\ge0\)

=>\(\frac{20\cdot\left(5x+1\right)-17x}{20x}\ge0\)

=>\(\frac{83x+20}{x}\ge0\)

TH1: \(\begin{cases}83x+20\ge0\\ x>0\end{cases}\Rightarrow\begin{cases}x\ge-\frac{20}{83}\\ x>0\end{cases}\Rightarrow x>0\)

TH2: \(\begin{cases}83x+20\le0\\ x<0\end{cases}\Rightarrow\begin{cases}83x\le-20\\ x<0\end{cases}\Rightarrow x\le-\frac{20}{83}\)

1.

- Với \(x\ge\frac{1}{2}\Rightarrow2x-1\le x+2\Rightarrow x\le3\Rightarrow\frac{1}{2}\le x\le3\)

- Với \(x< \frac{1}{2}\Rightarrow1-2x\le x+2\Rightarrow3x\ge-1\Rightarrow x\ge-\frac{1}{3}\)

Vậy nghiệm của BPT là \(-\frac{1}{3}\le x\le3\)

2.

Để pt có 2 nghiệm trái dấu

\(\Leftrightarrow ac< 0\Leftrightarrow\left(m+2\right)\left(2m-3\right)< 0\Rightarrow-2< m< \frac{3}{2}\)

3.

\(5x-1>\frac{2x}{5}+3\Leftrightarrow5x-\frac{2x}{5}>4\Leftrightarrow\frac{23}{5}x>4\Rightarrow x>\frac{20}{23}\)

4.

\(4x^2+4x+1-3x+9>4x^2+10\)

\(\Leftrightarrow x>0\)

5.

\(1< \frac{1}{1-x}\Leftrightarrow\frac{1}{1-x}-1>0\Leftrightarrow\frac{x}{1-x}>0\Rightarrow0< x< 1\)

6.

\(\frac{\left(x-5\right)^2\left(x-3\right)}{x+1}\le0\Rightarrow\left[{}\begin{matrix}x=5\\-1< x\le3\end{matrix}\right.\)

Cậu tách ra `2->3` câu thôi nhe

a: =>17x-5x-15-2x-5=0

=>10x-20=0

=>x=2

b: =>\(\dfrac{3x-6-5x-10}{\left(x+2\right)\left(x-2\right)}=\dfrac{11x+23}{\left(x+2\right)\left(x-2\right)}\)

=>11x+23=-2x-16

=>13x=-39

=>x=-3(nhận)

c: =>5x+7>=3x-3

=>2x>=-10

=>x>=-5

d: =>5(3x-1)=-2(x+1)

=>15x-5=-2x-2

=>17x=3

=>x=3/17

e: =>4x^2-1-4x^2-3x-2=0

=>-3x-3=0

=>x=-1

g: =>7x-5-8x+2-7<0

=>-x-10<0

=>x+10>0

=>x>-10

a: =>17x-5x-15-2x-5=0

=>10x-20=0

=>x=2

b: =>\(\dfrac{3x-6-5x-10}{\left(x+2\right)\left(x-2\right)}=\dfrac{11x+23}{\left(x+2\right)\left(x-2\right)}\)

=>11x+23=-2x-16

=>13x=-39

=>x=-3(nhận)

c: =>5x+7>=3x-3

=>2x>=-10

=>x>=-5

d: =>5(3x-1)=-2(x+1)

=>15x-5=-2x-2

=>17x=3

=>x=3/17

e: =>4x^2-1-4x^2-3x-2=0

=>-3x-3=0

=>x=-1

g: =>7x-5-8x+2-7<0

=>-x-10<0

=>x+10>0

=>x>-10

a: \(\Leftrightarrow4\left(5x^2-3\right)+5\left(3x-1\right)< 10x\left(2x+3\right)-100\)

\(\Leftrightarrow20x^2-12x+15x-5< 20x^2+30x-100\)

=>3x-5<=30x-100

=>30x-100>3x-5

=>27x>95

hay x>95/27

b: \(\Leftrightarrow4\left(5x-2\right)-6\left(2x^2-x\right)< 4x\left(1-3x\right)-15x\)

\(\Leftrightarrow20x-8-12x^2+6x< 4x-12x^2-15x\)

=>26x-8<-11x

=>37x<8

hay x<8/37

roois vãi

-Đăng tách câu hỏi bạn nhé.

rối thế bn