2-7x≥4x-4
Giải bpt
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Giải BPT
a, |x-4|+7x ≥ x²+12
b, |x²-3x+2|+x-2 ≤ 0
c, |x-3|/ x²-5x+6 ≥ 2
d, |x²-4x/ x²+x+2 ≤1
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giải hệ BPT :
\(\left\{{}\begin{matrix}3x^2-7x+2>0\\\left(4x-5\right)\left(-x^2-3x+4\right)\ge0\end{matrix}\right.\)
\(\left(4x-5\right)\left(-x^2-3x+4\right)>=0\)
\(\Leftrightarrow\left(4x-5\right)\left(x^2+3x-4\right)< =0\)
=>(4x-5)(x+4)(x-1)<=0
BXD:
Theo BXD, ta được: x<=-4 hoặc 1<=x<=5/4
\(3x^2-7x+2>0\)
=>3x2-6x-x+2>0
=>(x-2)(3x-1)>0
=>x>2 hoặc x<1/3
=>x<=-4
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Giải các BPT sau:
a) \(x^4\ge\left(x^2+4x+2\right)^2\)
b) \(x^2-7x+10< 0\)
1.giải các bpt sau
a.\(\left(x-3\right)\left(x+3\right)\ge x^2-7x+1\)
b.\(\dfrac{1,5-x}{5}\ge\dfrac{4x+5}{2}\)
2.giải các pt sau
\(x^3+1=x.\left(x+1\right)\)
Giai các bpt sau
a,\(\dfrac{x-1}{2}-\dfrac{7x+3}{15}\le\dfrac{2x+1}{3}+\dfrac{3-2x}{5}\)
b,\(\dfrac{2x+1}{-3}-\dfrac{2x^2+3}{-4}>\dfrac{x\left(5-3x\right)}{-6}-\dfrac{4x+1}{-5}\)
a: \(\Leftrightarrow15\left(x-1\right)-2\left(7x+3\right)\le10\left(2x+1\right)+6\left(3-2x\right)\)
\(\Leftrightarrow15x-15-14x-6\le20x+10+18-12x\)
=>x-21<=8x+28
=>-7x<=49
hay x>=-7
b: \(\Leftrightarrow20\left(2x+1\right)-15\left(2x^2+3\right)< 10x\left(5-3x\right)-12\left(4x+1\right)\)
\(\Leftrightarrow40x+20-30x^2-45< 50x-30x^2-48x-12\)
=>40x-25<2x-12
=>38x<13
hay x<13/38
\(a,\dfrac{x-1}{2}-\dfrac{7x+3}{15}\le\dfrac{2x+1}{3}+\dfrac{3-2x}{5}\\ \Leftrightarrow\dfrac{15\left(x-1\right)}{30}-\dfrac{2\left(7x+3\right)}{30}\le\dfrac{10\left(2x+1\right)}{30}+\dfrac{6\left(3-2x\right)}{30}\\ \Leftrightarrow15x-15-14x-6\le20x+10+18-12x\\ \Leftrightarrow x-21\le8x+28\\ \Leftrightarrow7x+49\ge0\\ \Leftrightarrow x\ge-7\)
\(b,\dfrac{2x+1}{-3}-\dfrac{2x^2+3}{-4}>\dfrac{x\left(5-3x\right)}{-6}-\dfrac{4x+1}{-5}\\ \Leftrightarrow\dfrac{20\left(2x+1\right)}{-60}-\dfrac{15\left(2x^2+3\right)}{-60}>\dfrac{10x\left(5-3x\right)}{-60}-\dfrac{12\left(4x+1\right)}{-60}\\ \Leftrightarrow40x+20-30x^2-45>50x-30x^2-48x-12\\ \Leftrightarrow38x-13>0\\ \Leftrightarrow x>\dfrac{13}{38}\)
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Giải bpt
1, \(\left|4x-3\right|=\left|4x+1\right|\)
2, \(\left|7x-1\right|=\left|7x+3\right|\)
3, \(\left|x+2\right|-3\left|x-1\right|< 2\left(x+4\right)\)
4, \(\left|x+5\right|-\left|x-7\right|< 4\)
1: |4x-3|=|4x+1|
=>4x-3=4x+1 hoặc 4x-3=-4x-1
=>8x=2
hay x=1/4
2: |7x-1|=|7x+3|
=>7x+3=7x-1 hoặc 7x+3=1-7x
=>14x=-2
hay x=-1/7
4: Trường hợp 1: x<-5
Pt sẽ là -x-5-(7-x)<4
=>-x-5-7+x<4
=>-12<4(loại)
Trường hợp 2: -5<=x<7
Pt sẽ là x+5-(7-x)<4
=>x+5-7+x<4
=>2x-2<4
=>2x<6
hay x<3
=>-5<=x<3
TH3: x>=7
Pt sẽlà x+5-(x-7)<4
=>x+5-x+7<4
=>12<4(vô lý)
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câu 1:giải các pt và bpt sau: a,17x - 5(x+3)= 2x + 5 b,3/x+2 - 5/x-2 = 11x + 23/(x+2)(x-2) c,5x + 7 ≥ 3(x-1) d,3x-1/x+1 = -2/5 e,(2x-1)(2x+1)= 4x2 + 3x + 2 f,x-3^3 -7+3x g,7x-5 < 2(4x-1)+7
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
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câu 1:giải các pt và bpt sau:
a,17x - 5(x+3)= 2x + 5
b,3/x+2 - 5/x-2 = 11x + 23/(x+2)(x-2)
c,5x + 7 ≥ 3(x-1)
d,3x-1/x+1 = -2/5
e,(2x-1)(2x+1)= 4x2 + 3x + 2
f,x-3^3 -7+3x
g,7x-5 < 2(4x-1)+7
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
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giải bpt bậc hai : x2-7x+22≤0
