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\(a,\dfrac{2}{3}x-\dfrac{2}{5}=\dfrac{1}{2}x-\dfrac{1}{3}\\ \Rightarrow\dfrac{2}{3}x-\dfrac{1}{2}x-\dfrac{2}{5}=-\dfrac{1}{3}\\ \Rightarrow x\left(\dfrac{2}{3}-\dfrac{1}{2}\right)-\dfrac{2}{5}=-\dfrac{1}{3}\\ \Rightarrow x\dfrac{1}{6}=-\dfrac{11}{15}\\ \Rightarrow x=-\dfrac{22}{5}\\ b,\dfrac{1}{3}x+\dfrac{2}{5}.\left(x+1\right)=0\\ \Rightarrow\dfrac{1}{3}x+\left(x+1\right)=-\dfrac{2}{5}\\ \Rightarrow\dfrac{1}{3}x=-\dfrac{2}{5}-\left(x+1\right)\\ \Rightarrow\dfrac{1}{3}x=-\dfrac{7}{5}-x\\ \Rightarrow\dfrac{1}{3}.2x=-\dfrac{7}{5}\\ \Rightarrow2x=-\dfrac{21}{5}\\ \Rightarrow x=-\dfrac{21}{10}.\)
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Ta có:\(\hept{\begin{cases}\left|x-1,5\right|\ge0\\\left|y-2,3\right|\ge0\end{cases}\Rightarrow\left|x-1,5\right|+\left|y-2,3\right|\ge0}\)
Dấu "=" xảy ra khi \(\hept{\begin{cases}\left|x-1,5\right|=0\\\left|y-2,3\right|=0\end{cases}\Rightarrow\hept{\begin{cases}x=1,5\\y=2,3\end{cases}}}\)
b,tương tự
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a, \(\left(5x-1\right)\left(2x-\frac{1}{3}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}5x-1=0\\2x-\frac{1}{3}=0\end{cases}\Rightarrow}\orbr{\begin{cases}5x=1\\2x=\frac{1}{3}\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{1}{5}\\x=\frac{1}{6}\end{cases}}\)
b. \(\left(x^2+1\right)\left(x-4\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^2+1=0\\x-4=0\end{cases}\Rightarrow}\orbr{\begin{cases}x^2=-1\left(Voly\right)\\x=4\end{cases}\Rightarrow x=4}\)
c, \(2x^2-\frac{1}{3}x=0\)
\(\Leftrightarrow x\left(2x-\frac{1}{3}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\2x-\frac{1}{3}=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=\frac{1}{6}\end{cases}}\)
d, \(\left(\frac{4}{5}\right)^{5x}=\left(\frac{4}{5}\right)^7\)
\(\Rightarrow5x=7\)
\(\Rightarrow x=\frac{7}{5}\)
e, Ta có: \(A=\frac{x+5}{x-2}=\frac{\left(x-2\right)+7}{x-2}=1+\frac{7}{x-2}\)
Để A ∈ Z <=> (x - 2) ∈ Ư(7) = { ±1; ±7 }
x - 2 | 1 | -1 | 7 | -7 |
x | 3 | 1 | 9 | -5 |
Vậy....
a) \(\left(5x-1\right)\left(2x-\frac{1}{3}\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}5x-1=0\\2x-\frac{1}{3}=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}5x=1\\2x=\frac{1}{3}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{5}\\x=\frac{1}{6}\end{cases}}\)
Vậy : ....
b) \(\left(x^2+1\right)\left(x-4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^2+1=0\\x-4=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x^2=-1\left(loại\right)\\x=4\end{cases}}\)
c) \(2x^2-\frac{1}{3}x=0\)
\(\Leftrightarrow x\left(2x-\frac{1}{3}\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\2x-\frac{1}{3}=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=\frac{1}{6}\end{cases}}\)
Vậy :...
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Mk sẽ giải từng câu
\(a)\) \(\left(3x+1\right)\left(x-2\right)>0\)
Trường hợp 1 :
\(\hept{\begin{cases}3x+1>0\\x-2>0\end{cases}\Leftrightarrow\hept{\begin{cases}3x>-1\\x>2\end{cases}\Leftrightarrow}\hept{\begin{cases}x>\frac{-1}{3}\\x>2\end{cases}}}\)
\(\Rightarrow\)\(x>2\)
Trường hợp 2 :
\(\hept{\begin{cases}3x+1< 0\\x-2< 0\end{cases}\Leftrightarrow\hept{\begin{cases}3x< -1\\x< 2\end{cases}\Leftrightarrow}\hept{\begin{cases}x< \frac{-1}{3}\\x< 2\end{cases}}}\)
\(\Rightarrow\)\(x< \frac{-1}{3}\)
Vậy \(x>2\) hoặc \(x< \frac{-1}{3}\) thì \(\left(3x+1\right)\left(x-2\right)>0\)
Chúc bạn học tốt ~
a) (3x+1).(x-2)>0
TH1: 3x+1>0 TH2: x-2>0
3x > -1 x>2
x>-1/3
Vậy x>2
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\(a,\frac{1}{3}+\frac{1}{2}:x=\frac{1}{5}\)
\(\Leftrightarrow\frac{1}{2}:x=\frac{1}{5}-\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{2}:x=\frac{3}{15}-\frac{5}{15}\)
\(\Leftrightarrow\frac{1}{2}:x=\frac{-2}{15}\)
\(\Leftrightarrow x=\frac{1}{2}:\frac{-15}{2}=\frac{-15}{4}\)
\(b,\frac{1}{3}x+\frac{2}{5}\left[x+1\right]=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x+\frac{2}{5}=0\)
\(\Leftrightarrow\frac{11}{15}x=-\frac{2}{5}\Leftrightarrow x=\frac{-2}{5}:\frac{11}{15}=\frac{-2}{5}\cdot\frac{15}{11}=\frac{-2}{1}\cdot\frac{3}{11}=\frac{-6}{11}\)
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\(\left(\frac{2}{3}x-\frac{1}{5}\right).\left(\frac{3}{5}x+\frac{2}{3}\right)< 0\)
\(TH1:\frac{2}{3}x-\frac{1}{5}< 0\)
\(\frac{2}{3}x< \frac{1}{5}\)
\(x< \frac{1}{5}:\frac{2}{3}\)
\(x< \frac{3}{10}\)
\(TH2:\frac{3}{5}x+\frac{2}{3}< 0\)
\(\frac{3}{5}x< \frac{-2}{3}\)
\(x< \frac{-2}{3}:\frac{3}{5}\)
\(x< \frac{-10}{9}\)
vậy ....
hc tốt
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B1: Đk: 5x ≥ 0 => x ≥ 0
Vì |x + 1| ≥ 0 => |x + 1| = x + 1
|x + 2| ≥ 0 => |x + 2| = x + 2
|x + 3| ≥ 0 => |x + 3| = x + 3
|x + 4| ≥ 0 => |x + 4| = x + 4
=> |x + 1| + |x + 2| + |x + 3| + |x + 4| = 5x
=> x + 1 + x + 2 + x + 3 + x + 4 = 5x
=> 4x + 10 = 5x
=> x = 10
B2: Ta có: |x - 2018| = |2018 - x|
=> A=|x + 2000| + |2018 - x| ≥ |x + 2000 + 2018 - x| = |4018| = 4018
Dấu " = " xảy ra <=> (x + 2000)(x - 2018) ≥ 0
Th1: \(\hept{\begin{cases}x+2000\ge0\\x-2018\ge0\end{cases}\Rightarrow}\hept{\begin{cases}x\ge-2018\\x\le2018\end{cases}}\Rightarrow-2018\le x\le2018\)
Th2: \(\hept{\begin{cases}x+2000\le0\\x-2018\le0\end{cases}\Rightarrow}\hept{\begin{cases}x\le-2018\\x\ge2018\end{cases}}\)(vô lý)
Vậy GTNN của A = 4018 khi -2018 ≤ x ≤ 2018
B3:
a, Vì |x + 1| ≥ 0 ; |2y - 4| ≥ 0
=> |x + 1| + |2y - 4| ≥ 0
Dấu " = " xảy ra <=> \(\hept{\begin{cases}x+1=0\\2y-4=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x=-1\\y=2\end{cases}}\)
Vậy...
b, Vì |x - y + 1| ≥ 0 ; (y - 3)2 ≥ 0
=> |x - y + 1| + (y - 3)2 ≥ 0
Dấu " = " xảy ra <=> \(\hept{\begin{cases}x-y+1=0\\y-3=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x-y=-1\\y=3\end{cases}}\Leftrightarrow\hept{\begin{cases}x-3=-1\\y=3\end{cases}\Leftrightarrow}\hept{\begin{cases}x=2\\y=3\end{cases}}\)
Vậy...
c, Vì |x + y| ≥ 0 ; |x - z| ≥ 0 ; |2x - 1| ≥ 0
=> |x + y| + |x - z| + |2x - 1| ≥ 0
Dấu " = " xảy ra <=> \(\hept{\begin{cases}x+y=0\\x-z=0\\2x-1=0\end{cases}\Leftrightarrow\hept{\begin{cases}x+y=0\\x=z\\x=\frac{1}{2}\end{cases}\Leftrightarrow}}\hept{\begin{cases}\frac{1}{2}+y=0\\x=z=\frac{1}{2}\end{cases}\Leftrightarrow}\hept{\begin{cases}y=\frac{-1}{2}\\x=z=\frac{1}{2}\end{cases}}\)
Từ đề bài ta có x - 1 3 = 0 hoặc x+ 2 5 =0. Tìm được x = 1 3 hoặc x= - 2 5