giải bất phương trình sau:
a) 5 - 7x \(\ge\) 2x + 14
b) \(\dfrac{1,5-x}{5}\)< \(\dfrac{4x+5}{2}\)
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Giải bất phương trình
\(\dfrac{x^2+2x+2}{x+1}\ge\dfrac{x^2+4x+5}{x+1}-1\)
ĐKXĐ : x khác -1
\(\dfrac{x^2+2x+2}{x+1}\ge\dfrac{x^2+3x+4}{x+1}\\ \Leftrightarrow\dfrac{x^2+2x+2}{x+1}\ge\dfrac{x^2+2x+2}{x+1}+\dfrac{x+2}{x+1}\\ \Leftrightarrow\dfrac{x+2}{x+1}\le0\\ \Leftrightarrow x+2\ge0;x+1< 0\Leftrightarrow-1>x\ge-2\)
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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
\(x^3+1=x.\left(x+1\right)\)
giải các bất phương trình sau
a)\(\dfrac{2-x}{3}< \dfrac{3-2x}{5}\)
b)\(\dfrac{2x+15}{9}\ge\dfrac{x-1}{5}+\dfrac{x}{3}\)
a: =>5(2-x)<3(3-2x)
=>10-5x<9-6x
=>x<-1
b: =>2/9x+5/3>=1/5x-1/5+1/3x
=>2/9x+5/3>=8/15x-1/5
=>-14/45x>=-28/15
=>x<=6
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Giải các phương trình sau:a.dfrac{5x-2}{3}dfrac{5-3x}{2}b.dfrac{10x+3}{12}1+dfrac{6+8x}{9}c.2left(x+dfrac{3}{5}right)5-left(dfrac{13}{5}+xright)d.dfrac{7}{8}x-5left(x-9right)dfrac{20x+1,5}{6}e.dfrac{7x-1}{6}+2xdfrac{16-x}{5}f.dfrac{x+4}{5}-x+4dfrac{x}{3}-dfrac{x-2}{2}
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Giải các phương trình sau:
\(a.\dfrac{5x-2}{3}=\dfrac{5-3x}{2}\)
\(b.\dfrac{10x+3}{12}=1+\dfrac{6+8x}{9}\)
\(c.2\left(x+\dfrac{3}{5}\right)=5-\left(\dfrac{13}{5}+x\right)\)
\(d.\dfrac{7}{8}x-5\left(x-9\right)=\dfrac{20x+1,5}{6}\)
\(e.\dfrac{7x-1}{6}+2x=\dfrac{16-x}{5}\)
\(f.\dfrac{x+4}{5}-x+4=\dfrac{x}{3}-\dfrac{x-2}{2}\)
a: =>10x-4=15-9x
=>19x=19
hay x=1
b: \(\Leftrightarrow3\left(10x+3\right)=36+4\left(8x+6\right)\)
=>30x+9=36+32x+24
=>30x-32x=60-9
=>-2x=51
hay x=-51/2
c: \(\Leftrightarrow2x+\dfrac{6}{5}=5-\dfrac{13}{5}-x\)
=>3x=6/5
hay x=2/5
d: \(\Leftrightarrow\dfrac{7x}{8}-\dfrac{5\left(x-9\right)}{1}=\dfrac{20x+1.5}{6}\)
\(\Leftrightarrow21x-120\left(x-9\right)=4\left(20x+1.5\right)\)
=>21x-120x+1080=80x+60
=>-179x=-1020
hay x=1020/179
e: \(\Leftrightarrow5\left(7x-1\right)+60x=6\left(16-x\right)\)
=>35x-5+60x=96-6x
=>95x+6x=96+5
=>x=1
f: \(\Leftrightarrow6\left(x+4\right)+30\left(-x+4\right)=10x-15\left(x-2\right)\)
=>6x+24-30x+120=10x-15x+30
=>-24x+96=-5x+30
=>-19x=-66
hay x=66/19
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Giải các bất phương trình tích , bất phương trình thương sau
a) \(4x^{2^{ }}-4x+1>9\)
b)\(\left(x-5\right)\left(7-2x\right)\le0\)
c)\(\dfrac{x+1}{5-x}\le0\)
d)\(\dfrac{x+2}{4-x}\ge0\)
e)\(\dfrac{-7x+14}{\left(x+5\right)\left(2x-3\right)}>0\)
Bạn Kim Tuyến làm sai rùi , mk sửa lại :
a) 4x2 - 4x + 1 > 9
⇔ 4x2 - 4x - 8 > 0
⇔4x2 + 4x - 8x - 8 > 0
⇔ 4x( x + 1) -8( x + 1) > 0
⇔ ( x + 1)( 4x - 8) > 0
⇔ ( x + 1)( x - 2) > 0
Lập bảng xét dấu , ta có :
Vậy, nghiệm của BPT : x < -1 hoặc : x > 2
b) ( x - 5)( 7 - 2x ) < 0
Lập bảng xét dấu :
Vậy , nghiệm của BPT : x < 7/2 hoặc x > 5
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a) 4\(x^2\)-4x+1>9
<=> (4x-1)\(^2\)>9
<=> 4x-1>\(\pm\)3
*4x-1>3 *4x-1>-3
<=>4x>3+1 <=> 4x>-3+1
<=>4x>4 <=> 4x>-2
<=>x>1 <=>x>\(\dfrac{-1}{2}\)
b)(x−5)(7−2x)≤0
<=>(x-5)\(\le\)0 hoặc (7-2x)\(\le\)0
* x-5\(\le\)0 *7-2x\(\le\)0
<=> x\(\le\)5 <=>-2x\(\le\)-7
<=> x\(\ge\)\(\dfrac{7}{2}\)
c)\(\dfrac{x+1}{5-x}\)\(\le\)0
<=> x+1\(\le\)0
<=> x\(\le\)-1
d)\(\dfrac{x+2}{4-x}\)\(\ge\)0
<=> x+2\(\ge\)0
<=> x\(\ge\)-2
e)\(\dfrac{-7x+14}{\left(x+5\right)\left(2x-3\right)}\)>0
<=> -7x+14>0
<=>-7x>-14
<=>x<2
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Giải các bất phương trình :
a) \(\dfrac{2-x}{4}< 5\)
b) \(3\le\dfrac{2x+3}{5}\)
c) \(\dfrac{4x-5}{3}>\dfrac{7-x}{5}\)
d) \(\dfrac{2x+3}{-4}\ge\dfrac{4-x}{-3}\)
bài 2 giải các phương trình saub,dfrac{2left(3-7xright)}{1+x}dfrac{1}{2} m,dfrac{3x-1}{x+1}dfrac{2x+1}{x-1}d,dfrac{3x-14}{x+5}dfrac{2}{3} p,dfrac{4x+7}{x-1}dfrac{12x+5}{3x+4}f,dfrac{6}{x}-1dfrac{2x-3}{3} r,dfrac{1}{x+3}+dfrac{1}{x-1}dfrac{10}{left(x+3right)left(x-1right)}h,dfrac{1}{x-2}+3dfrac{x-3}{2-x} t,dfrac{3x}{x-2}-dfrac{x}{x-5}dfrac{3x}{left(x-2right)left(5-xright)}j,dfrac{5}{3x+2}2x-1 u,dfrac{x+3}{x+1}+dfrac{x-2}{x}dfrac{2...
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bài 2 giải các phương trình sau
b,\(\dfrac{2\left(3-7x\right)}{1+x}=\dfrac{1}{2}\) m,\(\dfrac{3x-1}{x+1}=\dfrac{2x+1}{x-1}\)
d,\(\dfrac{3x-14}{x+5}=\dfrac{2}{3}\) p,\(\dfrac{4x+7}{x-1}=\dfrac{12x+5}{3x+4}\)
f,\(\dfrac{6}{x}-1=\dfrac{2x-3}{3}\) r,\(\dfrac{1}{x+3}+\dfrac{1}{x-1}=\dfrac{10}{\left(x+3\right)\left(x-1\right)}\)
h,\(\dfrac{1}{x-2}+3=\dfrac{x-3}{2-x}\) t,\(\dfrac{3x}{x-2}-\dfrac{x}{x-5}=\dfrac{3x}{\left(x-2\right)\left(5-x\right)}\)
j,\(\dfrac{5}{3x+2}=2x-1\) u,\(\dfrac{x+3}{x+1}+\dfrac{x-2}{x}=\dfrac{2\left(x^2+x-1\right)}{x\left(x+1\right)}\)
w,\(\dfrac{5x}{2x+2}+1=-\dfrac{6}{x+1}\) s, \(\dfrac{6}{x-1}-\dfrac{4}{x-3}=\dfrac{2x}{\left(x-1\right)\left(x-3\right)}\)
ơ,\(\dfrac{1}{x-1}+\dfrac{2}{x+1}=\dfrac{x}{x^2-1}\) v,\(\dfrac{x}{2\left(x-3\right)}+\dfrac{x}{2\left(x+1\right)}=\dfrac{2x}{\left(x+1\right)\left(x-3\right)}\)
z,\(\dfrac{1}{x-1}-\dfrac{3x^2}{x^3-1}=\dfrac{2x}{x^2+x+1}\) ư,\(\dfrac{x+2}{x-2}-\dfrac{-2}{x^2-2x}=\dfrac{1}{x}\)
o,\(x+\dfrac{1}{x}=x^2+\dfrac{1}{x^2}\) ô,\(1-\dfrac{1}{1-x}=\dfrac{x^2}{x^2-1}\) zz,\(\dfrac{12}{8+x^3}=1+\dfrac{1}{x+2}\)
b: =>\(4\left(3-7x\right)=x+1\)
=>12-28x=x+1
=>-29x=-11
=>x=11/29
m:=>(3x-1)(x-1)=(2x+1)(x+1)
=>3x^2-4x+1=2x^2+3x+1
=>x^2-7x=0
=>x=0 hoặcx=7
d: =>9x-42=2x+10
=>7x=52
=>x=52/7
p: \(\Leftrightarrow\left(4x+7\right)\left(3x+4\right)=\left(12x+5\right)\left(x-1\right)\)
=>12x^2+16x+21x+28=12x^2-12x+5x-5
=>37x+28=7x-5
=>30x=-33
=>x=-11/10
j: =>(2x-1)(3x+2)=5
=>6x^2+4x-3x-2-5=0
=>6x^2-x-7=0
=>6x^2-7x+6x-7=0
=>(6x-7)(x+1)=0
=>x=7/6 hoặc x=-1
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Giải các bất phương trình, hệ phương trìnha) dfrac{x^2-4x+3}{2x-3}ge x-1b) 3x^2-left|4x^2+x-5right|3c)4x-left|2x^2-8x-15right|le-1d)x+3-sqrt{21-4x-x^2}ge0e)left{{}begin{matrix}xleft(x+5right) 4x+2left(2x-1right)left(x+3right)ge4xend{matrix}right.f)dfrac{1}{x^2-5x+4}ledfrac{1}{x^2-7x+10}
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Giải các bất phương trình, hệ phương trình
a) \(\dfrac{x^2-4x+3}{2x-3}\ge x-1\)
b) \(3x^2-\left|4x^2+x-5\right|>3\)
c)\(4x-\left|2x^2-8x-15\right|\le-1\)
d)\(x+3-\sqrt{21-4x-x^2}\ge0\)
e)\(\left\{{}\begin{matrix}x\left(x+5\right)< 4x+2\\\left(2x-1\right)\left(x+3\right)\ge4x\end{matrix}\right.\)
f)\(\dfrac{1}{x^2-5x+4}\le\dfrac{1}{x^2-7x+10}\)
Giải các phương trình sau:
\(a.\dfrac{4x-5}{x-1}=2+\dfrac{x}{x-1}\)
\(b.\dfrac{7}{x+2}=\dfrac{3}{x-5}\)
\(c.\dfrac{14}{3x-12}-\dfrac{2+x}{x-4}=\dfrac{3}{8-2x}-\dfrac{5}{6}\)
\(d.\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{16}{x^2-1}\)
TK
https://lazi.vn/edu/exercise/giai-phuong-trinh-4x-5-x-1-2-x-x-1-7-x-2-3-x-5
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a: \(\Leftrightarrow4x-5=2x-2+x\)
=>4x-5=3x-2
=>x=3(nhận)
b: =>7x-35=3x+6
=>4x=41
hay x=41/4(nhận)
c: \(\Leftrightarrow\dfrac{14}{3\left(x-4\right)}-\dfrac{x+2}{x-4}=\dfrac{-3}{2\left(x-4\right)}-\dfrac{5}{6}\)
\(\Leftrightarrow\dfrac{28}{6\left(x-4\right)}-\dfrac{6\left(x+2\right)}{6\left(x-4\right)}=\dfrac{-9}{6\left(x-4\right)}-\dfrac{5\left(x-4\right)}{6\left(x-4\right)}\)
\(\Leftrightarrow28-6x-12=-9-5x+20\)
=>-6x+16=-5x+11
=>-x=-5
hay x=5(nhận)
d: \(\Leftrightarrow x^2+2x+1-\left(x^2-2x+1\right)=16\)
\(\Leftrightarrow4x=16\)
hay x=4(nhận)
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