(-3x-1) (-1 phần 2x cộng 5)=0
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20 tháng 5 2022
a: 3-2|4x-5|=2/6
=>2|4x-5|=3-1/3=8/3
=>|4x-5|=4/3
=>4x-5=4/3 hoặc 4x-5=-4/3
=>4x=19/3 hoặc 4x=11/3
=>x=19/12 hoặc x=11/12
c: (7-3x)(2x+1)=0
=>2x+1=0 hoặc -3x+7=0
=>x=-1/2 hoặc x=-7/3
d: 2x(5-3x)>0
=>x(3x-5)<0
=>0<x<5/3
HL
5 tháng 7 2017
a) * Nếu 4x - 5 \(\ge\) 0 thì x \(\ge\) \(\dfrac{5}{4}\)
\(\Leftrightarrow\) \(3-2\left(4x-5\right)=\dfrac{2}{6}\)
\(\Leftrightarrow\) \(-8x=-3-10+\dfrac{2}{6}\)
\(\Leftrightarrow\) x = \(\dfrac{19}{12}\) (t/m)
* Nếu 4x - 5 < 0 thì x < \(\dfrac{5}{4}\)
\(\Leftrightarrow\) \(3-2\left(-4x+5\right)=\dfrac{2}{6}\)
\(\Leftrightarrow\) \(3+8x-10=\dfrac{2}{6}\)
\(\Leftrightarrow\) x = \(\dfrac{11}{12}\) (t/m)
b) Không hiểu đề :v
c) \(\left(7-3x\right)\left(2x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}7-3x=0\\2x+1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{3}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
d) \(2x\left(5-3x\right)>0\)
\(\Rightarrow\left\{{}\begin{matrix}2x>0\\5-3x>0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x>0\\x< \dfrac{5}{3}\end{matrix}\right.\)
\(\Rightarrow0< x< \dfrac{5}{3}\)
e) \(\left(4-2x\right)\left(5x+3\right)< 0\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}4-2x< 0\\5x+3>0\end{matrix}\right.\\\left\{{}\begin{matrix}4-2x>0\\5x+3< 0\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>2\\x< -\dfrac{3}{5}\end{matrix}\right.\\\left\{{}\begin{matrix}x< 2\\x>-\dfrac{3}{5}\end{matrix}\right.\end{matrix}\right.\)
Loại TH1, nhận TH2
Vậy \(-\dfrac{3}{5}< x< 2\)
g) \(\left|3x+1\right|+\left|1-3x\right|=0\) (1)
* Nếu x < \(\dfrac{-1}{3}\)
PT (1) \(\Leftrightarrow-3x-1-1+3x=0\)
0x - 2 = 0
0x = 2 \(\Rightarrow\) PT vô nghiệm
* Nếu \(\dfrac{-1}{3}\le x\le\dfrac{1}{3}\)
PT (1) \(\Leftrightarrow3x+1-1+3x=0\)
6x = 0
x = 0 (t/m)
* Nếu x > \(\dfrac{1}{3}\)
PT (1) \(\Leftrightarrow3x+1+1-3x=0\)
0x + 2 = 0
0x = -2
PT vô nghiệm.
Vậy x = 0
5 tháng 7 2017
a, \(3-2\left|4x-5\right|=\dfrac{2}{6}\)
\(\Rightarrow2\left|4x-5\right|=\dfrac{8}{3}\)
\(\Rightarrow\left|4x-5\right|=\dfrac{4}{3}\)
+) Xét \(x\ge\dfrac{5}{4}\) có:
\(4x-5=\dfrac{4}{3}\Rightarrow4x=\dfrac{19}{3}\Rightarrow x=\dfrac{19}{12}\) ( t/m )
+) Xét \(x< \dfrac{5}{4}\) có:
\(4x-5=\dfrac{-4}{3}\Rightarrow4x=\dfrac{11}{3}\Rightarrow x=\dfrac{11}{12}\) ( t/m )
Vậy...
b, tương tự
c, \(\left(7-3x\right)\left(2x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}7-3x=0\\2x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{3}\\x=\dfrac{-1}{2}\end{matrix}\right.\)
Vậy...
d, \(2x\left(5-3x\right)>0\)
\(\Rightarrow\left\{{}\begin{matrix}2x>0\\5-3x>0\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}2x< 0\\5-3x< 0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x>0\\x< \dfrac{3}{5}\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}x< 0\\x>\dfrac{3}{5}\end{matrix}\right.\) (loại )
Vậy \(0< x< \dfrac{3}{5}\)
e, tương tự
g, \(\left|3x+1\right|+\left|1-3x\right|=0\)
\(\Rightarrow\left|3x+1\right|+\left|3x-1\right|=0\)
+) Xét \(x\ge\dfrac{1}{3}\) có:
\(3x+1+3x-1=0\)
\(\Rightarrow6x=0\)
\(\Rightarrow x=0\) ( ko t/m )
+) Xét \(\dfrac{-1}{3}\le x< \dfrac{1}{3}\) có:
\(3x+1+1-3x=0\)
\(\Rightarrow2=0\) ( vô lí )
+) Xét \(x< \dfrac{-1}{3}\) có:
\(-3x-1+1-3x=0\)
\(\Rightarrow-6x=0\Rightarrow x=0\) ( ko t/m )
Vậy ko có giá trị x thỏa mãn đề bài
PD
1
GH
12 tháng 2 2018
a) \(4x-3=11-3x\)
\(\Leftrightarrow4x+3x=11+3\)
\(\Leftrightarrow7x=14\)
\(\Leftrightarrow x=2\)
Vậy .............
b) \(x^3-4x^2+3x=0\)
\(\Leftrightarrow x\left(x^2-4x+3\right)=0\)
\(\Leftrightarrow x\left(x^2-x-3x+3\right)=0\)
\(\Leftrightarrow x\left[x\left(x-1\right)-3\left(x-1\right)\right]=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-1=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=3\end{matrix}\right.\)
Vậy .................
P/s: câu c bn gõ lại dc ko
LT
0
29 tháng 11 2021
\(\dfrac{3-3x}{2x}+\dfrac{3x-1}{2x-1}+\dfrac{11x-5}{2x-4x^2}\\ =\dfrac{\left(3-3x\right)\left(1-2x\right)}{2x\left(1-2x\right)}-\dfrac{2x\left(3x-1\right)}{2x\left(1-2x\right)}+\dfrac{11x-5}{2x\left(1-2x\right)}\\ =\dfrac{3-9x+6x^2}{2x\left(1-2x\right)}-\dfrac{6x^2-2x}{2x\left(1-2x\right)}+\dfrac{11x-5}{2x\left(1-2x\right)}\\ =\dfrac{3-9x+6x^2-6x^2+2x+11x-5}{2x\left(1-2x\right)}\\ =\dfrac{-2}{2x\left(1-2x\right)}\\ =\dfrac{-1}{x\left(1-2x\right)}\)
22 tháng 10 2019
1. \(6x^3-8=40\\ 6x^3=48\\ x^3=8\\ \Rightarrow x=2\)Vậy x = 2
2. \(4x^5+15=47\\ 4x^5=32\\ x^5=8\\ \Rightarrow x\in\varnothing\left(\text{vì }x\in N\right)\)Vậy x ∈ ∅
3. \(2x^3-4=12\\ 2x^3=16\\ x^3=8\\ \Rightarrow x=2\)Vậy x = 2
4. \(5x^3-5=0\\ 5x^3=5\\ x^3=1\\ \Rightarrow x=1\)Vậy x = 1
5. \(\left(x-5\right)^{2016}=\left(x-5\right)^{2018}\\ \Rightarrow\left[{}\begin{matrix}x-5=0\\x-5=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)Vậy \(x\in\left\{5;6\right\}\)
6. \(\left(3x-2\right)^{20}=\left(3x-1\right)^{20}\\ \Rightarrow3x-2=3x-1\\ 3x-3x=2-1\\ 0=1\left(\text{vô lí}\right)\)Vậy x ∈ ∅
7. \(\left(3x-1\right)^{10}=\left(3x-1\right)^{20}\\ \left(3x-1\right)^{10}=\left[\left(3x-1\right)^2\right]^{10}\\ \Rightarrow\left(3x-1\right)^2=3x-1\\ \left(3x-1\right)^2-\left(3x-1\right)=0\\ \left(3x-1\right)\left[\left(3x-1\right)-1\right]=0\\ \left(3x-1\right)\left(3x-2\right)=0\\ \Rightarrow\left[{}\begin{matrix}3x-1=0\\3x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}3x=1\\3x=2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{1}{3}\left(\text{loại vì }x\in N\right)\\x=\frac{2}{3}\left(\text{loại vì }x\in N\right)\end{matrix}\right.\)Vậy x ∈ ∅
8. \(\left(2x-1\right)^{50}=2x-1\\ \left(2x-1\right)^{50}-\left(2x-1\right)=0\\ \left(2x-1\right)\left[\left(2x-1\right)^{49}-1\right]=0\\ \Rightarrow\left[{}\begin{matrix}2x-1=0\\\left(2x-1\right)^{49}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=1\\2x-1=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\frac{1}{2}\left(\text{loại vì }x\in N\right)\\x=1\left(t/m\right)\end{matrix}\right.\)Vậy x = 1
9. \(\left(\frac{x}{3}-5\right)^{2000}=\left(\frac{x}{3}-5\right)^{2008}\\ \left(\frac{x}{3}-5\right)^{2008}-\left(\frac{x}{3}-5\right)^{2000}=0\\ \left(\frac{x}{3}-5\right)^{2000}\left[\left(\frac{x}{3}-5\right)^8-1\right]=0\\ \Rightarrow\left[{}\begin{matrix}\left(\frac{x}{3}-5\right)^{2000}=0\\\left(\frac{x}{3}-5\right)^8=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}\frac{x}{3}-5=0\\\frac{x}{3}-5=1\\\frac{x}{3}-5=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}\frac{x}{3}=5\\\frac{x}{3}=6\\\frac{x}{3}=4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\cdot3=15\\x=6\cdot3=18\\x=4\cdot3=12\end{matrix}\right.\)Vậy \(x\in\left\{15;18;12\right\}\)
22 tháng 10 2019
\(1.6x^3-8=40\\ \Leftrightarrow6x^3=48\\ \Leftrightarrow x^3=8\Leftrightarrow x^3=2^3=\left(-2\right)^3\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
Vậy \(x\in\left\{2;-2\right\}\)
\(2.4x^3+15=47\) (T nghĩ đề là mũ 3)
\(\Leftrightarrow4x^3=32\Leftrightarrow x^3=8=2^3=\left(-2\right)^3\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
Vậy \(x\in\left\{2;-2\right\}\)
Câu 3, 4 tương tự nhé.
(-3x - 1) (-1/2x+5) = 0
\(\Rightarrow\hept{\begin{cases}-3x-1=0\\\frac{-1}{2x}+5=0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=\frac{1}{3}\\\frac{-1}{2x}=-5\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=\frac{1}{3}\\x=\frac{2}{5}\end{cases}}\)