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\(\Leftrightarrow3\left(1-2x\right)-2\left(x+1\right)< =6\)
=>3-6x-2x-2<=6
=>-8x+1<=6
=>-8x<=5
hay x>=5/8
\(\frac{x+4}{5}+\frac{3x+2}{10}< \frac{x-1}{3}\)
\(\Leftrightarrow\frac{6\left(x+4\right)}{30}+\frac{3\left(3x+2\right)}{30}< \frac{10\left(x-1\right)}{30}\)
\(\Leftrightarrow6x+24+9x+6< 10x-10\)
\(\Leftrightarrow5x+40< 0\)
\(\Leftrightarrow x< -8\)
Tự biểu diễn nha bạn
\(\frac{x+4}{5}+\frac{3x+2}{10}< \frac{x-1}{3}\)
\(\Rightarrow\frac{6\left(x+4\right)}{30}+\frac{3\left(3x+2\right)}{30}< \frac{10\left(x-1\right)}{30}\)
\(\Rightarrow6x+24+9x+6< 10x-10\)
\(5x< -40\)
\(\Rightarrow x< -8\)
Ta có: \(\dfrac{x-1}{3}-\dfrac{3x+5}{2}\ge1-\dfrac{4x+5}{6}\)
\(\Leftrightarrow2\left(x-1\right)-3\left(3x+5\right)\ge6-4x-5\)
\(\Leftrightarrow2x-2-9x-15-6+4x+5\ge0\)
\(\Leftrightarrow-3x\ge18\)
hay \(x\le-6\)
\(x^2-4x+3\ge0\)
\(\left(x-1\right)\left(x-3\right)\ge0\)
TH1; X-1>=0 VA X-3>=0
TH2: X-1=<0 VA X-3<=0
Vay x>=3 hoac x<=1
a)
\(\dfrac{2\left(x+1\right)}{3}-2\ge\dfrac{x-2}{2}\)
\(\Leftrightarrow\dfrac{2\left(x+1\right)\cdot2}{6}-\dfrac{6}{6}-\dfrac{3\left(x-2\right)}{6}\ge0\)
\(\Leftrightarrow\dfrac{4x+4-6-3x+6}{6}\ge0\)
\(\Leftrightarrow\dfrac{x+4}{6}\ge0\)
\(\Leftrightarrow x+4\ge0\Leftrightarrow x\ge-4\)
b) Tự biểu diễn
\(\dfrac{2x-3}{2}>\dfrac{1-3x}{6}\)
\(\Leftrightarrow\dfrac{3\left(2x-3\right)}{6}>\dfrac{1-3x}{6}\)
\(\Leftrightarrow6x-9>1-3x\)
\(\Leftrightarrow6x+3x>1+9\)
\(\Leftrightarrow9x>10\)
\(\Leftrightarrow x>\dfrac{10}{9}\)
Vậy BPT có nghiệm \(x>\dfrac{10}{9}\)
> 0 10/9 ( ///////////////////////
\(\dfrac{x+1}{3}>\dfrac{2x-1}{6}-2\)
\(\Leftrightarrow2\left(x+1\right)>2x-1-12\)
\(\Leftrightarrow2x+2>2x-13\) \(\Leftrightarrow2x-2x>-13-2\)
\(\Leftrightarrow0x>-15\) ( luôn đúng)
Vậy bpt trên có vô số nghiệm
\(\Rightarrow\) k cần phải biểu diễn trên trục số
\(1-2\left(x+1\right)\ge5\left(x-2\right)+2\)
\(\Leftrightarrow1-2x-2\ge5x-10+2\)
\(\Leftrightarrow-2x-5x\ge-10+2-1+2\)
\(\Leftrightarrow-7x\ge-7\)
\(\Leftrightarrow x\le1\)
\(\frac{3x+3}{3x-2}< 1\)
\(\Leftrightarrow\frac{3x-2+5}{3x-2}< 1\)
\(\Leftrightarrow1+\frac{5}{3x-2}< 1\)
\(\Leftrightarrow\frac{5}{3x-2}< 0\)
\(\Leftrightarrow3x-2< 0\)
\(\Leftrightarrow3x< 2\)
\(\Leftrightarrow x< \frac{2}{3}\)
\(\dfrac{x-2}{2}+1\le\dfrac{x-1}{3}\)
\(\Leftrightarrow\dfrac{3\left(x-2\right)}{6}+\dfrac{1.6}{6}\le\dfrac{2\left(x-1\right)}{6}\)
`<=> 3x - 6 + 6 <= 2x-2`
`<=> 3x <= 2x-2`
`<=> 3x -2x <= -2`
`<=> x <= -2`
\(\dfrac{x-2}{2}\)+1≤\(\dfrac{x-1}{3}\)
<=>\(\dfrac{3x-6}{6}\)+\(\dfrac{6}{6}\)≤\(\dfrac{2x-1}{6}\)
<=>3x-6+6≤2x-1
<=>x<-1