1)Rút gọn biểu thức sau theo chuyên đề bất đẳng thức
A=|7-5x|-|3x-7|-2x+1
B=7x-|4-3x|+5
2)Tìm giá trị của x để
x>2x
a+x<a
\(x^3>x^2\)
3)tìm các số a,b,c không âm sao cho a+3c=8,a+2b=9 và tổng a+b+c có giá trị lớn nhất
4)Tìm x sao cho
a)1-2x<7
b)(x-1)(x-2)>0
c)\(\left(x-2\right)^2\)(x+1)(x+4)<0
d)\(\dfrac{x^2\left(x+3\right)}{x-9}< 0\)
e)\(\dfrac{5}{x}< 1\)
f)\(\dfrac{2x-5}{x-1}< 0\)
5)Tìm các số nguyên a sao cho
\(\left(a^2-1\right)\left(a^2-4\right)\left(a^2-7\right)\left(a^2-10\right)< 0\)
6)Tìm giá trị của x để
A=\(\dfrac{x+5}{x+3}< 1\)
B=\(\dfrac{x+3}{x+4}>1\)
C=\(\dfrac{x+1}{\dfrac{2}{3}-x}>0\)
D=\(\dfrac{x-5}{x+5}\)<0
E=\(\dfrac{3x+4}{5-2x}\)>0
Help me mai 25/7 bảy giờ tối mik đi học rồi ai giúp mik được mấy câu thì giúp
Mik cảm ơn nha
Nhiều quá, từng bài 1 nhé, bài nào làm được, tớ sẽ cố gắng.
bài 2:
a) \(x>2x\Leftrightarrow x-2x>0\Leftrightarrow-x>0\Leftrightarrow x< 0\)
Kl: x<0
b) \(a+x< a\Leftrightarrow x< 0\)
Kl: x<0
c) \(x^3>x^2\Leftrightarrow x^3-x^2>0\Leftrightarrow x^2\left(x-1\right)>0\) (*)
Mà x^2 > 0 \(\Rightarrow\) (*) \(\Leftrightarrow x-1>0\Leftrightarrow x>1\)
Kl: x>1
Câu 4:
a) \(1-2x< 7\Leftrightarrow2x>-6\Leftrightarrow x>3\)
Kl: x>3
b) \(\left(x-1\right)\left(x-2\right)>0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\\x-2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\\x-2< 0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>1\\x>2\end{matrix}\right.\\\left\{{}\begin{matrix}x< 1\\x< 2\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x>2\\x< 1\end{matrix}\right.\)
Kl: x>2 hoặc x<1
c) \(\left(x-2\right)^2\left(x+1\right)\left(x+4\right)< 0\Leftrightarrow\left(x+1\right)\left(x+4\right)< 0\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1>0\\x+4< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x+1< 0\\x+4>0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-1\\x< -4\end{matrix}\right.\\\left\{{}\begin{matrix}x< -1\\x>-4\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}-1< x< -4\left(vô-lý\right)\\-4< x< -1\end{matrix}\right.\) \(\Leftrightarrow-4< x< -1\)
Kl: -4<x<-1
d) ĐK: x khác 9\(\dfrac{x^2\left(x+3\right)}{x-9}< 0\Leftrightarrow x^2\left(x+3\right)\left(x-9\right)< 0\Leftrightarrow\left(x+3\right)\left(x-9\right)< 0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+3>0\\x-9< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x+3< 0\\x-9>0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-3\\x< 9\end{matrix}\right.\\\left\{{}\begin{matrix}x< -3\\x>9\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}-3< x< 9\left(N\right)\\9< x< -3\left(vô-lý\right)\end{matrix}\right.\) \(\Leftrightarrow-3< x< 9\)
Kl: -3<x<9
e) Đk: x khác 0
\(\dfrac{5}{x}< 1\Leftrightarrow\dfrac{5}{x}< \dfrac{5}{5}\Leftrightarrow x>5\left(N\right)\)
KL: x >5
f) ĐK: x khác 1
\(\dfrac{2x-5}{x-1}< 0\Leftrightarrow\left(2x-5\right)\left(x-1\right)< 0\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-5>0\\x-1< 0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-5< 0\\x-1>0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>\dfrac{5}{2}\\x< 1\end{matrix}\right.\\\left\{{}\begin{matrix}x< \dfrac{5}{2}\\x>1\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\dfrac{5}{2}< x< 1\left(vô-lý\right)\\1< x< \dfrac{5}{2}\left(N\right)\end{matrix}\right.\)
Kl: 1< x< 5/2
Bài 6:
a) ĐK: x khác -3
\(\dfrac{x+5}{x+3}< 1\Leftrightarrow x+5< x+3\Leftrightarrow0< -2\left(vô-lý\right)\)
Kl: bpt vn
b) ĐK: x khác -4
\(\dfrac{x+3}{x+4}>1\Leftrightarrow x+3>x+4\Leftrightarrow0>1\left(vô-lý\right)\)
Kl: bpt vn
c) Đk: x khác 2/3
\(\dfrac{x+1}{\dfrac{2}{3}-x}>0\Leftrightarrow\left(x+1\right)\left(\dfrac{2}{3}-x\right)>0\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1>0\\\dfrac{2}{3}-x>0\end{matrix}\right.\\\left\{{}\begin{matrix}x+1< 0\\\dfrac{2}{3}-x< 0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-1\\x< \dfrac{2}{3}\end{matrix}\right.\\\left\{{}\begin{matrix}x< -1\\x>\dfrac{2}{3}\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}-1< x< \dfrac{2}{3}\left(N\right)\\\dfrac{2}{3}< x< -1\left(vô-lý\right)\end{matrix}\right.\)
Kl: \(-1< x< \dfrac{2}{3}\)
d) x khác -5
\(\dfrac{x-5}{x+5}< 0\Leftrightarrow\left(x-5\right)\left(x+5\right)< 0\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-5>0\\x+5< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x-5< 0\\x+5>0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>5\\x< -5\end{matrix}\right.\\\left\{{}\begin{matrix}x< 5\\x>-5\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}5< x< -5\left(vô-lý\right)\\-5< x< 5\left(N\right)\end{matrix}\right.\)
Kl: -5<x<5
e) Đk: x khác 5/2
\(\dfrac{3x+4}{5-2x}>0\Leftrightarrow\left(3x+4\right)\left(5-2x\right)>0\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3x+4>0\\5-2x>0\end{matrix}\right.\\\left\{{}\begin{matrix}3x+4< 0\\5-2x< 0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-\dfrac{4}{3}\\x< \dfrac{5}{2}\end{matrix}\right.\\\left\{{}\begin{matrix}x< -\dfrac{4}{3}\\x>\dfrac{5}{2}\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}-\dfrac{4}{3}< x< \dfrac{5}{2}\left(N\right)\\\dfrac{5}{2}< x< -\dfrac{4}{3}\left(vô-lý\right)\end{matrix}\right.\)
Kl: -4/3 <x< 5/2
