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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 :
x x+1 x-2 -1 2 0 0 - + + - - + Tích số + - + 0 0 Vậy, nghiệm của BPT : x < -1 hoặc : x > 2
b) ( x - 5)( 7 - 2x ) < 0
Lập bảng xét dấu :
x x-5 7-2x tích số 7/2 5 0 0 0 0 - - + + - - - + - Vậy , nghiệm của BPT : x < 7/2 hoặc x > 5
a)
\(4x-10< 0\\ 4x< 10\\ x< \dfrac{10}{4}=\dfrac{5}{2}\)
b)
\(2x+x+12\ge0\\ 3x\ge-12\\ x\ge-\dfrac{12}{3}=-4\)
c)
\(x-5\ge3-x\\ 2x\ge8\\ x\ge4\)
d)
\(7-3x>9-x\\ -2>2x\\ x< -1\)
đ)
\(2x-\left(3-5x\right)\le4\left(x+3\right)\\ 2x-3+5x\le4x+12\\ 3x\le15\\ x\le5\)
e)
\(3x-6+x< 9-x\\ 5x< 15\\ x< 3\)
f)
\(2t-3+5t\ge4t+12\\ 3t\ge15\\ t\ge5\)
g)
\(3y-2\le2y-3\\ y\le-1\)
h)
\(3-4x+24+6x\ge x+27+3x\\ 0\ge2x\\ 0\ge x\)
i)
\(5-\left(6-x\right)\le4\left(3-2x\right)\\ 5-6+x\le12-8x\\ \\ 9x\le13\\ x\le\dfrac{13}{9}\)
k)
\(5\left(2x-3\right)-4\left(5x-7\right)\ge19-2\left(x+11\right)\\ 10x-15-20x+28\ge19-2x-22\\ 13-10x\ge-2x-3\\ -8x\ge-16\\ x\le\dfrac{-16}{-8}=2\)
l)
\(\dfrac{2x-5}{3}-\dfrac{3x-1}{2}< \dfrac{3-x}{5}-\dfrac{2x-1}{4}\\ \dfrac{40x-100}{60}-\dfrac{90x-30}{2}< \dfrac{36-12x}{60}-\dfrac{30x-15}{60}\\ \Rightarrow40x-100-90x+30< 36-12x-30x+15\\ 130-50x< 51-42x\\ 92x< -79\\ x< -\dfrac{79}{92}\)
m)
\(5x-\dfrac{3-2x}{2}>\dfrac{7x-5}{2}+x\\ \dfrac{10x}{2}-\dfrac{3-2x}{2}>\dfrac{7x-5}{2}+\dfrac{2x}{2}\\ \Rightarrow10x-3+2x>7x-5+2x\\ 12x-3>9x-5\\ 3x>-2\\ x>-\dfrac{2}{3}\)
n)
\(\dfrac{7x-2}{3}-2x< 5-\dfrac{x-2}{4}\\ \dfrac{28x-8}{12}-\dfrac{24x}{12}< \dfrac{60}{12}-\dfrac{3x-6}{12}\\ \Rightarrow28x-8-24x< 60-3x+6\\ 4x-8< -3x+66\\ 7x< 74\\ x< \dfrac{74}{7}\)
a) \(4x-10< 0\)
\(\Leftrightarrow4x< 10\)
\(\Leftrightarrow x< \dfrac{5}{2}\)
b) ???
c) \(x-5\ge3-x\)
\(\Leftrightarrow2x-5\ge3\)
\(\Leftrightarrow2x\ge8\)
\(\Leftrightarrow x\ge4\)
d) \(7-3x>9-x\)
\(\Leftrightarrow7-2x>9\)
\(\Leftrightarrow-2x>2\)
\(\Leftrightarrow x< -1\)
đ) ???
e) \(3x-6+x< 9-x\)
\(\Leftrightarrow4x-6< 9-x\)
\(\Leftrightarrow5x-6< 9\)
\(\Leftrightarrow5x< 15\)
\(\Leftrightarrow x< 3\)
f) ???
g) ???
h) \(3-4x+24+6x\ge x+27+3x\)
\(\Leftrightarrow2x+27\ge4x+27\)
\(\Leftrightarrow-2x\ge0\)
\(\Leftrightarrow x\le0\)
i) \(5-\left(6-x\right)\le4\left(3-2x\right)\)
\(\Leftrightarrow5-6+x\le12-8x\)
\(\Leftrightarrow x-1\le12-8x\)
\(\Leftrightarrow9x-1\le12\)
\(\Leftrightarrow9x\le13\)
\(\Leftrightarrow x\le\dfrac{13}{9}\)
k) \(5\left(2x-3\right)-4\left(5x-7\right)\ge19-2\left(x+11\right)\)
\(\Leftrightarrow10x-15-20x+28\ge19-2x-22\)
\(\Leftrightarrow-10x+23\ge-3-2x\)
\(\Leftrightarrow-8x+13\ge-3\)
\(\Leftrightarrow-8x\ge-16\)
\(\Leftrightarrow x\ge2\)
l) \(\dfrac{2x-5}{3}-\dfrac{3x-1}{2}< \dfrac{3-x}{5}-\dfrac{2x-1}{4}\)
\(\Leftrightarrow-\dfrac{5}{6}x-\dfrac{7}{6}< -\dfrac{7}{10}x+\dfrac{17}{20}\)
\(\Leftrightarrow-\dfrac{2}{15}x-\dfrac{7}{6}< \dfrac{17}{20}\)
\(\Leftrightarrow-\dfrac{2}{15}x< \dfrac{121}{60}\)
\(\Leftrightarrow x>-\dfrac{121}{8}\)
m, n) làm tương tự:
đáp án: m. \(x>-\dfrac{2}{3}\); n. \(x< \dfrac{74}{7}\)
\(a,2x+7\ge0\Leftrightarrow2x\ge-7\Rightarrow x\ge\dfrac{-7}{2}\)
\(b,5-2x\le0\Leftrightarrow-2x\le-5\Leftrightarrow x\ge\dfrac{5}{2}\)
\(c,\dfrac{x+2}{x^2+1}\ge0\Leftrightarrow x+2\ge x^2+1\Leftrightarrow x+2-x^2-1\ge0\Leftrightarrow x-x^2+1\ge0\)\(\Leftrightarrow-\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{5}{4}\ge0\Leftrightarrow-\left(x-\dfrac{1}{2}\right)^2\ge-\dfrac{5}{4}\Rightarrow\left(x-\dfrac{1}{2}\right)^2\ge\dfrac{5}{4}\)\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{1}{2}\ge\sqrt{\dfrac{5}{4}}\\x-\dfrac{1}{2}\ge-\sqrt{\dfrac{5}{4}}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x\ge\sqrt{\dfrac{5}{4}}+\dfrac{1}{2}\\x\ge-\sqrt{\dfrac{5}{4}}+\dfrac{1}{2}\end{matrix}\right.\)
\(d,\dfrac{x^2+3}{2-x}< 0\Leftrightarrow x^2+3< 2-x\Leftrightarrow x^2+3-2+x\ge0\Leftrightarrow\left(x^2+x+\dfrac{1}{4}\right)+\dfrac{3}{4}\ge0\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2\ge\dfrac{-3}{4}\)( vô lí )
Vậy : BPT trên vô nghiệm
a: \(x< -9:\dfrac{3}{2}=-9\cdot\dfrac{2}{3}=-6\)
b: 2/3x>-2
hay x>-2:2/3=-3
c: \(2x>\dfrac{9}{5}-\dfrac{4}{5}=1\)
hay x>1/2
d: \(\Leftrightarrow x\cdot\dfrac{3}{5}>6-4=2\)
hay x>2:3/5=2x5/3=10/3
a: =>3x-1>8
=>3x>9
hay x>3
b: \(\Leftrightarrow2x+4< 9\)
=>2x<5
hay x<5/2
c: \(\Leftrightarrow1-2x>12\)
=>-2x>11
hay x<-11/2
d: \(\Leftrightarrow6-4x< 5\)
=>-4x<-1
hay x>1/4
\(a,\dfrac{3\left(5x-2\right)}{4}-2=\dfrac{7x}{3}-5\left(x-7\right)\)
\(\Leftrightarrow\dfrac{15x-6-8}{4}=\dfrac{7x-15\left(x-7\right)}{3}\)
\(\Leftrightarrow\dfrac{15x-14}{4}=\dfrac{7x-15x+105}{3}\)
\(\Leftrightarrow\dfrac{45x-42}{12}=\dfrac{-32x+420}{12}\)
\(\Leftrightarrow45x+32x=420+42\)
\(\Leftrightarrow77x=462\)
\(\Leftrightarrow x=6\)
\(b,\dfrac{x+5}{2}+\dfrac{3-2x}{4}=x-\dfrac{7+x}{6}\)
\(\Leftrightarrow\dfrac{2x+10+3-2x}{4}=\dfrac{6x-7-x}{6}\)
\(\Leftrightarrow\dfrac{13}{4}=\dfrac{5x-7}{6}\)
\(\Leftrightarrow2\left(5x-7\right)=3.13\)
\(\Leftrightarrow10x-14=39\)
\(\Leftrightarrow10x=53\)
\(\Leftrightarrow x=5,3\)
\(c,\dfrac{x-3}{11}+\dfrac{x+1}{3}=\dfrac{x+7}{9}-1\)
\(\Leftrightarrow\dfrac{3x-9+11x+11}{33}=\dfrac{x+7-9}{9}\)
\(\Leftrightarrow\dfrac{14x+2}{33}=\dfrac{x-2}{9}\)
\(\Leftrightarrow33\left(x-2\right)=9\left(14x+2\right)\)
\(\Leftrightarrow33x-66=126x+18\)
\(\Leftrightarrow-93x=84\)
\(\Leftrightarrow x=-\dfrac{28}{31}\)
\(d,\dfrac{3x-0,4}{2}+\dfrac{1,5-2x}{3}=\dfrac{x+0,5}{5}\)
\(\Leftrightarrow\dfrac{3\left(3x-0,4\right)+2\left(1,5-2x\right)}{6}=\dfrac{x+0,5}{5}\)
\(\Leftrightarrow\dfrac{9x-1,2+3-4x}{6}=\dfrac{x+0,5}{5}\)
\(\Leftrightarrow\dfrac{5x+1,8}{6}=\dfrac{x+0,5}{5}\)
\(\Leftrightarrow5\left(5x+1,8\right)=6\left(x+0,5\right)\)
\(\Leftrightarrow25x+9=6x+3\)
\(\Leftrightarrow19x=-6\)
\(\Leftrightarrow x=-\dfrac{6}{19}\)
\(\Leftrightarrow77x=378\)
\(\Leftrightarrow x=\dfrac{54}{11}\)
a ) \(5-7x\ge2x+14\)
\(\Leftrightarrow-7x-2x\ge14-5\)
\(\Leftrightarrow-9x\ge9\)
\(\Leftrightarrow x\le-1\)
Vậy bất phương trình có nghiệm \(x\le1\)
b ) \(\dfrac{1,5-x}{5}< \dfrac{4x+5}{2}\)
\(\Leftrightarrow2\left(1,5-x\right)< 5\left(4x+5\right)\)
\(\Leftrightarrow3-2x< 20x+25\)
\(\Leftrightarrow-2x-20x< 25-3\)
\(\Leftrightarrow-22x< 22\)
\(\Leftrightarrow x>-1\)
Vậy bất phương trình có nghiệm \(x>-1\)
Tick nha
a) 5 - 7x \(\ge\) 2x + 14
\(\Leftrightarrow\) -7x -2x \(\ge\) -5 + 14
\(\Leftrightarrow\) -9x \(\ge\) 9
\(\Leftrightarrow\) x \(\le\) -1
b) \(\dfrac{1,5-x}{5}< \dfrac{4x+5}{2}\)
\(\Leftrightarrow\) \(2\left(1,5-x\right)\) \(< 5\left(4x+5\right)\)
\(\Leftrightarrow\) \(3-2x\)\(< 20x+25\)
\(\Leftrightarrow\) \(-2x-20x< -3+25\)
\(\Leftrightarrow\) \(-22x< 22\)
\(\Leftrightarrow\) \(x>-1\)