a) \(\frac{7-8x}{6}=\frac{-4+2x}{5}\)
=> \(\left(7-8x\right).5=6\left(-4+2x\right)\)
=> 35 - 40x = -24 + 12x
=> 35 + 24 = 12x + 40x
=> 52x = 59
=> x = 59/52
b) \(\frac{1-3:x}{8}=\frac{8}{1-3:x}\)
=> (1 - 3: x)2 = 82
=> \(\orbr{\begin{cases}1-3:x=8\\1-3:x=-8\end{cases}}\)
=> \(\orbr{\begin{cases}3:x=-7\\3:x=9\end{cases}}\)
=> \(\orbr{\begin{cases}x=-\frac{3}{7}\\x=\frac{1}{3}\end{cases}}\)
c) \(\left(x+1\right)\left(x-2\right)\ge0\)
=> \(\hept{\begin{cases}x+1\ge0\\x-2\ge0\end{cases}}\)hoặc \(\hept{\begin{cases}x+1\le0\\x-2\le0\end{cases}}\)
=> \(\hept{\begin{cases}x\ge-1\\x\ge2\end{cases}}\) hoặc \(\hept{\begin{cases}x\le-1\\x\le2\end{cases}}\)
=> \(-1\le x\le2\)
h) \(\left(x+1\right)\left(x-3\right)\le0\)
=> \(\hept{\begin{cases}x+1\ge0\\x-3\le0\end{cases}}\)hoặc \(\hept{\begin{cases}x+1\le0\\x-3\ge0\end{cases}}\)
=> \(\hept{\begin{cases}x\ge-1\\x\le3\end{cases}}\) hoặc \(\hept{\begin{cases}x\le-1\\x\ge3\end{cases}}\) (loại)
= \(-1\le x\le3\)
Mình làm tiếp bạn Edogawa Conan ! Hai bài a và c bạn ấy làm đúng rồi đó !
b, \(\frac{1-3\text{ : }x}{8}=\frac{8}{1-3\text{ : }x}\)
\(\Rightarrow\text{ }\left(1-3\text{ : }x\right)\text{ x }\left(1-3\text{ : }x\right)=8\text{ x }8\)
\(\text{ }\left(1-3\text{ : }x\right)^2=8^2\)
\(\Rightarrow\text{ }1-3\text{ : }x=8\)
\(3\text{ : }x=1-8\)
\(3\text{ : }x=-7\)
\(x=-\frac{7}{3}\)
b, \(\frac{1-3\text{ : }x}{8}=\frac{8}{1-3\text{ : }x}\)
\(\Rightarrow\text{ }\left(1-3\text{ : }x\right)\text{ x }\left(1-3\text{ : }x\right)=8\text{ x }8\)
\(\text{ }\left(1-3\text{ : }x\right)^2=8^2\)
\(\Rightarrow\text{ }1-3\text{ : }x=8\)
\(3\text{ : }x=1-8\)
\(3\text{ : }x=-7\)
\(x=-\frac{7}{3}\)
a) \(\frac{7-8x}{6}=\frac{-4+2x}{5}\)
\(\Rightarrow\frac{7-8x}{6}=\frac{2x-4}{5}\)
\(\Rightarrow5.\left(7-8x\right)=6.\left(2x-4\right)\)
\(\Rightarrow35-40x=12x-24\)
\(\Rightarrow-12x-40x=-35-24\)
\(\Rightarrow-52x=-69\)
\(\Rightarrow52x=69\)
\(\Rightarrow x=69:52\)
\(\Rightarrow x=\frac{3}{4}\)
b) \(\frac{1-3:x}{8}=\frac{8}{1-3:x}\)
\(\Rightarrow\left(1-3:x\right).\left(1-3:x\right)=8.8\)
\(\Rightarrow\left(1-3x\right)^2=8^2\)
\(\Rightarrow1-3x=\pm8\)
\(\Rightarrow\orbr{\begin{cases}1-3x=8\\1-3x=-8\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}3x=-7\\3x=9\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-\frac{7}{3}\\x=3\end{cases}}\)
c) \(\left(x+1\right).\left(x-2\right)\ge0\)
\(\Rightarrow\orbr{\begin{cases}\left(x+1\right).\left(x-2\right)>0\\\left(x+1\right).\left(x-2\right)=0\end{cases}}\)
\(\text{Nếu }\left(x+1\right).\left(x-2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+1=0\\x-2=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-1\\x=2\end{cases}}\Rightarrow x\in\left\{-1;2\right\}}\)
\(\text{Nếu }\left(x+1\right).\left(x-2\right)>0\)
\(\Rightarrow\hept{\begin{cases}x+1>0\\x-2>0\end{cases}\text{hoặc }\hept{\begin{cases}x+1< 0\\x-2< 0\end{cases}}}\)
\(\text{Nếu }\hept{\begin{cases}x+1>0\\x-2>0\end{cases}\Rightarrow\hept{\begin{cases}x>-1\\x>2\end{cases}\Rightarrow}}x>2\)
\(\text{Nếu }\hept{\begin{cases}x+1< 0\\x-2< 0\end{cases}\Rightarrow\hept{\begin{cases}x< -1\\x< 2\end{cases}\Rightarrow}x< -1}\)
\(\text{Vậy }x\in\left\{-1;2\right\}\text{hoặc }x< -1\text{hoặc }x>2\)
d) \(\left(x+1\right).\left(x-3\right)\le0\)
\(\Rightarrow\orbr{\begin{cases}\left(x+1\right).\left(x-3\right)=0\\\left(x+1\right).\left(x-3\right)< 0\end{cases}}\)
\(\text{Nếu }\left(x+1\right).\left(x-3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+1=0\\x-3=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-1\\x=3\end{cases}}}\)
\(\text{Nếu }\left(x+1\right).\left(x-3\right)< 0\)
\(\Rightarrow\hept{\begin{cases}x+1< 0\\x-3>0\end{cases}\text{hoặc }\hept{\begin{cases}x+1>0\\x-3< 0\end{cases}}}\)
\(\text{Nếu }\hept{\begin{cases}x+1< 0\\x-3>0\end{cases}\Rightarrow\hept{\begin{cases}x< -1\\x>3\end{cases}\Rightarrow}x\in\varnothing}\)
\(\text{Nếu }\hept{\begin{cases}x+1>0\\x-3< 0\end{cases}\Rightarrow\hept{\begin{cases}x>-1\\x< 3\end{cases}}\Rightarrow-1< x< 3}\)
\(\text{Vậy }x=-1\text{ hoặc }x=3\text{ hoặc }-1< x< 3\)
