tìm x biết
a, ( 2x- 3 ) ( x + 1 ) < 0
b, ( x - \(\frac{1}{2}\) ) ( x + 3 ) >0
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11 tháng 9 2016
a)\(\left(2x-3\right)\left(x+1\right)< 0\)
\(\Leftrightarrow\begin{cases}2x-3>0\\x+1< 0\end{cases}\) hoặc \(\begin{cases}2x-3< 0\\x+1>0\end{cases}\)
\(\Leftrightarrow\begin{cases}x>\frac{3}{2}\\x< -1\end{cases}\) (loại) hoặc \(\begin{cases}x< \frac{3}{2}\\x>-1\end{cases}\)
\(\Leftrightarrow-1< x< \frac{3}{2}\)
b) \(\left(x-\frac{1}{2}\right)\left(x+3\right)>0\)
\(\Leftrightarrow\begin{cases}x-\frac{1}{2}>0\\x+3>0\end{cases}\) hoặc \(\begin{cases}x-\frac{1}{2}< 0\\x+3< 0\end{cases}\)
\(\Leftrightarrow\begin{cases}x>\frac{1}{2}\\x>-3\end{cases}\) hoặc \(\begin{cases}x< \frac{1}{2}\\x< -3\end{cases}\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x>\frac{1}{2}\\x< -3\end{array}\right.\)
c) Sai đề phải là \(\frac{x}{\left(x+3\right)\left(x+7\right)}\)
Có: \(\frac{3}{\left(x+3\right)\left(x+5\right)}+\frac{5}{\left(x+5\right)\left(x+10\right)}+\frac{7}{\left(x+10\right)\left(x+17\right)}=\frac{x}{\left(x+3\right)\left(x+17\right)}\)
\(\Leftrightarrow\)\(\frac{1}{x+3}-\frac{1}{x+5}+\frac{1}{x+5}-\frac{1}{x+10}+\frac{1}{x+10}-\frac{1}{x+7}=\frac{x}{\left(x+3\right)\left(x+7\right)}\)
\(\Leftrightarrow\)\(\frac{1}{x+3}-\frac{1}{x+7}=\frac{x}{\left(x+3\right)\left(x+7\right)}\)
\(\Leftrightarrow\)\(\frac{4}{\left(x+3\right)\left(x+7\right)}=\frac{x}{\left(x+3\right)\left(x+7\right)}\)
\(\Leftrightarrow x=4\)
14 tháng 9 2021
a) \(2x\left(x-3\right)+3\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(2x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\2x+3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{3}{2}\end{matrix}\right.\)
b) \(x\left(3x-1\right)-5\left(1-3x\right)=0\)
\(\Leftrightarrow x\left(3x-1\right)+5\left(3x-1\right)=0\)
\(\Leftrightarrow\left(3x-1\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-1=0\\x+5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=-5\end{matrix}\right.\)
9 tháng 8 2016
\(\frac{1}{4}+\frac{1}{3}:2x=-5\)
\(\frac{1}{3}:2x=-5-\frac{1}{4}\)
\(\frac{1}{3}:2x=\frac{-21}{4}\)
\(2x=\frac{1}{3}:\frac{-21}{4}\)
\(2x=\frac{-4}{63}\)
\(x=\frac{-4}{63}:2\)
\(x=\frac{-2}{63}\)
\(\)
9 tháng 8 2016
\(\frac{1}{4}+\frac{1}{3}:2x=-5\)
\(\Rightarrow\frac{1}{3}:2x=-\frac{21}{4}\)
\(\Rightarrow2x=\frac{-4}{63}\)
\(\Rightarrow x=\frac{-2}{63}\)
\(\left(3x-\frac{1}{4}\right)\left(x+\frac{1}{2}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}3x-\frac{1}{4}=0\\x+\frac{1}{2}=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{1}{12}\\x=\frac{-1}{2}\end{cases}}}\)
\(\left(2x-5\right)\left(\frac{3}{2}x+9\right)\left(0,3x-12\right)=0\)
Th1 : \(2x-5=0\Rightarrow x=\frac{5}{2}\)
Th2 : \(\frac{3}{2}x+9=0\Rightarrow x=-6\)
Th3 : \(0,3x-12=0\Rightarrow x=\frac{12}{0,3}\)
ZH
2
HP
26 tháng 10 2021
a. 3x2 - 2x - 1 = 0
<=> 3x2 - 3x + x - 1 = 0
<=> 3x(x - 1) + (x - 1) = 0
<=> (3x + 1)(x - 1) = 0
<=> \(\left[{}\begin{matrix}3x+1=0\\x-1=0\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=1\end{matrix}\right.\)
b. \(\dfrac{x+1}{3}+\dfrac{2x+3}{5}=\dfrac{3}{4}\)
<=> \(\dfrac{20\left(x+1\right)}{60}+\dfrac{12\left(2x+3\right)}{60}=\dfrac{45}{60}\)
<=> 20x + 20 + 24x + 36 = 45
<=> 44x = -11
<=> x = \(-\dfrac{1}{4}\)
26 tháng 10 2021
a) \(3x^2-2x-1=0\) \(\Leftrightarrow\left(x-1\right)\left(3x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{3}\end{matrix}\right.\)
b) Pt\(\Rightarrow\)\(5\cdot4\left(x+1\right)+3\cdot4\cdot\left(2x+3\right)=3\cdot3\cdot5\)
\(\Leftrightarrow44x=-11\Rightarrow x=-\dfrac{1}{4}\)
11 tháng 2 2018
\(\left(\frac{1}{x+1}-\frac{3}{\left(x+1\right)\left(x^2-x+1\right)}+\frac{3}{x^2-x+1}\right).\frac{3\left(x^2-x+1\right)}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x+1}\)
\(\left(\frac{x^2-x+1}{x^3+1}-\frac{3}{x^3+1}+\frac{3\left(x+1\right)}{x^3+1}\right).\frac{3\left(x^2-x+1\right)}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x+1}\)
\(\left(\frac{x^2-x+1-3+3x+3}{x^3+1}\right).\frac{3\left(x^2-x+1\right)}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x+1}\)
tới đây bạn biến đổi tiếp, gõ = cái này lâu quá, gõ mathtype nhanh hơn
EC
9 tháng 8 2016
a)\(\frac{1}{4}+\frac{1}{3}:2x=-5\)
\(\frac{1}{3}:2x=-5-\frac{1}{4}\)
\(\frac{1}{3}:2x=-\frac{21}{3}\)
\(2x=\frac{1}{3}:\left(\frac{-21}{3}\right)\)
\(2x=-\frac{1}{21}\)
\(x=\frac{-1}{42}\)
b)\(\left(3x-\frac{1}{4}\right).\left(x+\frac{1}{2}\right)=0\)
\(\Rightarrow\left[\begin{array}{nghiempt}3x-\frac{1}{4}=0\\x+\frac{1}{2}=0\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}3x=\frac{1}{4}\\x=-\frac{1}{2}\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{1}{12}\\x=-\frac{1}{2}\end{array}\right.\)
c)\(\left(2x-5\right).\left(\frac{3}{2}x+9\right).\left(0,3x-12\right)=0\)
\(\Rightarrow\left[\begin{array}{nghiempt}2x-5=0\\\frac{3}{2}x+9=0\\0,3x-12=0\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}2x=5\\\frac{3}{2}x=-9\\0,3x=12\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{5}{2}\\x=-6\\x=40\end{array}\right.\)
9 tháng 8 2016
a) 1/4 + 1/3 : 2x = -5
=> 1/3 : 2x = -5 - 1/4
=> 1/3 : 2x = -21/4
=> 2x = 1/3 : (-21/4) = -4/63
=> x = -4/63 : 2 = -2/63
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
20 tháng 12 2023
a, 12 - (2\(x^2\) - 3) = 7
2\(x^2\) - 3 = 12 - 7
2\(x^2\) - 3 = 5
2\(x^2\) = 8
\(x^2\) = 4
\(\left[{}\begin{matrix}x=-2\\x=2\end{matrix}\right.\)
18 tháng 8 2021
Bài 1:
Ta có: \(4-2\left(x+1\right)=2\)
\(\Leftrightarrow2\left(x+1\right)=2\)
\(\Leftrightarrow x+1=1\)
hay x=0
Bài 2:
Ta có: \(\left|2x-3\right|-1=2\)
\(\Leftrightarrow\left|2x-3\right|=3\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=3\\2x-3=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)