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BPT \(\Leftrightarrow x>3\)

x+3>6 <=> x>3

-------0-----(3----->

\(x+3>6\)

\(\Leftrightarrow x>6-3\)

\(\Leftrightarrow x>3\)

Biểu diễn trên trục số:

`(x-2)/6 -(x-1)/3 < x/2`

`<=> (x-2)/6 -(2(x-1))/6 < (3x)/6`

`<=> x-2 - (2x-2) <3x`

`<=> x-2-2x+2<3x`

`<=> -x <3x`

`<=> -x-3x<0`

`<=> -4x<0`

`<=> x>0`

\(\dfrac{x-2}{6}\)-\(\dfrac{x-1}{3}\)<\(\dfrac{x}{2}\)

\(\dfrac{x-2}{6}\)-\(\dfrac{2\left(x-1\right)}{6}\)<\(\dfrac{6x}{6}\)

<=>x-2-2x+2<6x

<=>-7x<0

<=>x>0

vậy tập nghiệm của bất phương trình là

\(\left\{x|x>0\right\}\)

\(\dfrac{x-2}{6}-\dfrac{x-1}{3}< \dfrac{x}{2}\\ \Leftrightarrow\dfrac{x-2}{6}-\dfrac{\left(x-1\right)2}{3.2}< \dfrac{x.3}{2.3}\\ \Leftrightarrow x-2-2x+2< 3x\\ \Leftrightarrow x-2x-3x< -2\\ \Leftrightarrow-4x< -2\\ \Leftrightarrow x>\dfrac{1}{2}\)

Vậy bất phương trình có tập nghiệm là:

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

Biểu diễn:

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 \(x\le-6\)

a:=>3x=15

=>x=5

b: =>8-11x<52

=>-11x<44

=>x>-4

c: \(VT=\left(\dfrac{x^2-\left(x-6\right)^2}{x\left(x+6\right)\left(x-6\right)}\right)\cdot\dfrac{x\left(x+6\right)}{2x-6}+\dfrac{x}{6-x}\)

\(=\dfrac{12x-36}{2x-6}\cdot\dfrac{1}{x-6}-\dfrac{x}{x-6}=\dfrac{6}{x-6}-\dfrac{x}{x-6}=-1\)

\(2x+2x+1< 2x-9\)

\(\Leftrightarrow2x+1< -9\)

\(\Leftrightarrow2x< 9-1\Leftrightarrow2x< 8\)

\(\Leftrightarrow2x:2< 8:2\Leftrightarrow x< 4\)

\(4x+1< 2x-9\)

\(\Leftrightarrow4x+1-2x+9< 0\)

\(\Leftrightarrow2x+10< 0\)

\(\Leftrightarrow2x< -10\)

\(\Leftrightarrow x< -5\)

a: =>2x<=-8

=>x<=-4

b: =>x+5<0

=>x<-5

c: =>2x>8

=>x>4

d: =>3x>=9

=>x>=3

1:

a: =>3x=6

=>x=2

b: =>4x=16

=>x=4

c: =>4x-6=9-x

=>5x=15

=>x=3

d: =>7x-12=x+6

=>6x=18

=>x=3

2:

a: =>2x<=-8

=>x<=-4

b: =>x+5<0

=>x<-5

c: =>2x>8

=>x>4