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a)\(0,5x\left(3x-4\right)+1,5x\left(0,7-x\right)\ge0,32\)
\(\Leftrightarrow1,5x^2-2+1,05-1,5x^2\ge0,32\)
\(\Leftrightarrow1,5x^2-1,5x^2-2+1,05\ge0,32\)
\(\Leftrightarrow-0,95\ge0,32\)(vô lí)
Vậy bất phương trình vô nghiệm
b)\(5x\left(12x+7\right)-3x\left(20x-5\right)\le-100\)
\(\Leftrightarrow60x^2+35x-60x^2+15x\le-100\)
\(\Leftrightarrow50x\le-100\)
\(\Leftrightarrow x\le-2\)
Vậy bất phương trình có nghiệm là \(S=\left\{xIx\le-2\right\}\)
a, -2x>15 x>-15/2 c, th1 x+2>0 vs x+3 <0 suy ra x>-2 vs x<-3 . th2 x+2<0,x+3>0 suy ra x<-2 ,x>-3
b, 112-x2>0
x2<112 x<11
a) \(3x-8>5x+7\)
\(\Leftrightarrow-8>5x+7-3x\)
\(\Leftrightarrow-8>2x+7\)
\(\Leftrightarrow-8-7>2x\)
\(\Leftrightarrow-15>2x\)
\(\Leftrightarrow-\frac{15}{2}>x\)
\(\Rightarrow x< -\frac{15}{2}\)
b) \(\left(11-x\right)\left(11+x\right)>0\)
\(\Leftrightarrow x=\pm11\)
\(\Rightarrow-11< x< 11\)
c) \(\left(x+2\right)\left(x+3\right)< 0\)
\(\Leftrightarrow x=-2;-3\)
\(\Rightarrow-3< x< -2\)
a) \(5x\left(12x+7\right)-3x\left(20x-5\right)=-100\\ \Leftrightarrow60x^2+35x-60x^2+15x=-100\Leftrightarrow50x=-100\Leftrightarrow x=-2\)
b) câu này nó cứ lộn lộn kiểu gì ý:vvvvô tình muốn giúp nhưng đíu bt đúng hay sai:vv
\(6x\left(x-0,5\right)-0.3x\left(2x+1.3\right)=0,138\\ \Leftrightarrow6x^2-3x-0,6x^2-0,39x=0,138\Leftrightarrow5,4x^2-3,39x=0,138\)
tới này thôi:vvv
a: 3x-5>15-x
=>4x>20
hay x>5
b: \(3\left(x-2\right)\left(x+2\right)< 3x^2+x\)
=>3x2+x>3x2-12
=>x>-12
a) \(5x\left(x-3\right)^2-5\left(x-1\right)^3+15\left(x-4\right)\left(x+4\right)\le10\)
\(\Leftrightarrow5x\left(x^2-6x+9\right)-5\left(x^3-3x^2+3x-1\right)+15\left(x^2-16\right)\le10\)
\(\Leftrightarrow5x^3-30x^2+45x-5x^3+15x^2-15x+5+15x^2-240\le10\)
\(\Leftrightarrow\left(5x^3-5x^3\right)-\left(30x^2-15x^2-15x^2\right)-\left(45x-15x\right)+5-240\le10\)
\(\Leftrightarrow30x-235\le10\)
\(\Leftrightarrow30x\le10+235\)
\(\Leftrightarrow30x\le245\)
\(\Leftrightarrow30x:30\le245:30\)
\(\Leftrightarrow x\le\dfrac{49}{6}\)
Vậy nghiệm của bất phương trình là: \(x\le\dfrac{49}{6}\)
b) \(\left(3x-2\right)\left(9x^2+6x+4\right)+27x\left(\dfrac{1}{3}-x\right)\left(\dfrac{1}{2}+x\right)\ge1\)
\(\Leftrightarrow27x^3-8+27x\left(\dfrac{1}{9}-x^2\right)\ge1\)
\(\Leftrightarrow27x^3-8+3x-27x^3\ge1\)
\(\Leftrightarrow\left(27x^3-27x^3\right)-8+3x\ge1\)
\(\Leftrightarrow-8+3x\ge1\)
\(\Leftrightarrow3x\ge1+8\)
\(\Leftrightarrow3x\ge9\)
\(\Leftrightarrow3x:3\ge9:3\)
\(\Leftrightarrow x\ge3\)
Vậy nghiệm của bất phương trình là \(x\ge3\)
a: =>5x(x^2-6x+9)-5(x^3-3x^2+3x-1)+15(x^2-16)<=10
=>5x^3-30x^2+45x-5x^3+15x^2-15x+5+15x^2-240<=10
=>30x-235<=10
=>30x<=245
=>x<=49/6
b: =>27x^3-8+27x(1/9-x^2)>=1
=>27x^3-8+3x-27x^3>=1
=>3x>=9
=>x>=3
a: 3x-5>15-x
=>3x+x>15+5
=>4x>20
=>x>5
b: \(3\left(x-2\right)\left(x+2\right)<3x^2+x\)
=>\(3\left(x^2-4\right)<3x^2+x\)
=>\(3x^2-12-3x^2-x<0\)
=>-x-12<0
=>x+12>0
=>x>-12
c: \(\left(2x+1\right)^2+3x\left(1-x\right)\le\left(x+2\right)^2\)
=>\(4x^2+4x+1+3x-3x^2\le x^2+4x+4\)
=>\(x^2+7x+1\le x^2+4x+4\)
=>7x+1<=4x+4
=>7x-4x<=4-1
=>3x<=3
=>x<=1
d: \(\frac{5x-20}{3}-\frac{2x^2+x}{2}>\frac{x\left(1-3x\right)}{3}-\frac{5x}{4}\)
=>\(\frac{4\left(5x-20\right)-6\left(2x^2+x\right)}{12}>\frac{4x\left(1-3x\right)-15x}{12}\)
=>\(4\left(5x-20\right)-6\left(2x^2+x\right)>4x\left(1-3x\right)-15x\)
=>\(20x-80-12x^2-6x>4x-12x^2-15x\)
=>14x-80>-11x
=>25x>80
=>\(x>\frac{80}{25}=\frac{16}{5}\)
e: 4-2x<=3x-6
=>-2x-3x<=-6-4
=>-5x<=-10
=>x>=2
f: \(\left(x+4\right)\left(5x-1\right)>5x^2+16x+2\)
=>\(5x^2-x+20x-4>5x^2+16x+2\)
=>19x-4>16x+2
=>3x>6
=>x>2
g: \(x\left(2x-1\right)-8<5-2x\left(1-x\right)\)
=>\(2x^2-x-8<5-2x+2x^2\)
=>-x-8<-2x+5
=>-x+2x<5+8
=>x<13
h: \(\frac{3x-1}{4}-\frac{3\left(x-2\right)}{8}-1>\frac{5-3x}{2}\)
=>\(\frac{2\left(3x-1\right)}{8}-\frac{3\left(x-2\right)}{8}-\frac88>\frac{4\left(5-3x\right)}{8}\)
=>2(3x-1)-3(x-2)-8>4(5-3x)
=>6x-2-3x+6-8>20-12x
=>3x-4>20-12x
=>15x>24
=>\(x>\frac{24}{15}\)
=>x>1,6
a: =>1,5x^2-2x+1,2x-1,5x^2>=0,32
=>-0,8x>=0,32
=>x<=4
b: =>60x^2+35x-60x^2+15x<=-100
=>50x<=-100
=>x<=-2