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a) \(\left(\frac{4}{13}.\frac{6}{5}+\frac{4}{13}.\frac{2}{5}\right).\left(2x+1\right)^2=\frac{10}{13}\)
\(\left(\frac{4}{13}.\frac{8}{5}\right).\left(2x+1\right)^2=\frac{10}{13}\)
\(\frac{32}{65}.\left(2x+1\right)^2=\frac{10}{13}\)
\(\left(2x+1\right)^2=\frac{10}{13}\div\frac{32}{65}\)
\(\left(2x+1\right)^2=\frac{25}{16}\)
\(\Rightarrow2x+1\in\left\{\frac{5}{4};-\frac{5}{4}\right\}\)
\(\hept{\begin{cases}2x+1=\frac{5}{4}\\2x+1=-\frac{5}{4}\end{cases}\Rightarrow\hept{\begin{cases}2x=\frac{1}{4}\\2x=-\frac{9}{4}\end{cases}\Rightarrow}\hept{\begin{cases}x=\frac{1}{8}\\x=-\frac{9}{8}\end{cases}}}\)
Vậy \(x\in\left\{\frac{1}{8};-\frac{9}{8}\right\}\)
\(x^3-\frac{9}{16}.x=0\)
\(x\left(x^2-\frac{9}{16}\right)=0\)
\(\hept{\begin{cases}x=0\\x^2-\frac{9}{16}=0\end{cases}\Rightarrow\hept{\begin{cases}x=0\\x^2=\frac{9}{16}\end{cases}\Rightarrow}\hept{\begin{cases}x=0\\x=\pm\frac{3}{4}\end{cases}}}\)
Vậy \(x\in\left\{0;\frac{3}{4};-\frac{3}{4}\right\}\)
\(1,x.\left(x+7\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x+7=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=-7\end{cases}}}\)
\(2,\left(x+12\right).\left(x-3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+12=0\\x-3=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-12\\x=3\end{cases}}}\)
\(3,\left(-x+5\right).\left(3-x\right)=0\)
\(\Rightarrow\orbr{\begin{cases}-x+5=0\\3-x=0\end{cases}\Rightarrow\orbr{\begin{cases}-x=-5\\x=3\end{cases}\Rightarrow}\orbr{\begin{cases}x=5\\x=3\end{cases}}}\)
\(4,24:\left(3x-2\right)=-3\)
\(3x-2=-8\)
\(3x=-6\)
\(x=-2\)
\(5,-45:5\left(-3-2x\right)=3\)
\(5\left(-3-2x\right)=-15\)
\(-3-2x=-3\)
\(2x=0\)
\(x=0\)
\(6,x.\left(2+x\right)\left(7-x\right)=0\)
\(x=0\) hoặc \(\orbr{\begin{cases}2+x=0\\7-x=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-2\\x=7\end{cases}}}\)
\(7,\left(x-1\right)\left(x+2\right)\left(-x+3\right)=0\)
TH1: x-1=0 TH2 : x+2=0 TH3: -x+3=0
x=1 x=-2 -x=-3 => x=3
Bài 1
a,\(\left|x-3\right|=13+7=20\)
\(TH1:x-3=20\Rightarrow x=23\)
\(TH2:x-3=-20\Rightarrow x=-17\)
b,
TH1:\(x-2=3\Rightarrow x=5\)
TH2:\(x-2=-3\Rightarrow x=-1\)
a,| x-3|-7=13
=>|x-3| =13+7
=>|x-3| =20
=>x-3=20;-20
* x-3=20 *x-3=-20
=>x=20+3 =>x=-20+3
=>x=23 thuộc Z =>x=-17 thuộc Z
Vậy x=23 hoặc x=-17
a) Ta có: x + 34 là bội của x + 1
=> x + 34 \(⋮\)x + 1
=> (x + 1) + 33 \(⋮\)x + 1
=> 33 \(⋮\)x + 1
=> x + 1 \(\in\)Ư(33) = {1; 3; 11; 33}
Với: x + 1 = 1 => x = 1 - 1 = 0
x + 1 = 3 => x = 3 - 1 = 2
x + 1 = 11 => x = 11 - 1 = 10
x + 1 = 33 => x = 33 - 1 = 32
b) HD: 2x + 1 là ước của 4x + 82
=> 4x + 82 là B(2x + 1)
=> 2(2x + 1) + 80 \(⋮\)2x + 1
=> 80 \(⋮\)2x + 1 => 2x + 1 \(\in\)Ư(80) = {...} (tự liệt kê)
còn lại TT câu a
c) cx như trên
d) Ta có: 3x + 6 \(⋮\)2x - 1
=> 2(3x + 6) \(⋮\)2x - 1
=> 6x + 12 \(⋮\)2x - 1
=> 3(2x - 1) + 15 \(⋮\)2x - 1
=> 15 \(⋮\)2x - 1 => 2x - 1 \(\in\)Ư(15) = {1; 3; 5; 15}
còn lại tự lm (như trên)
a) 2x - 8 = 5
2x = 5 + 8
2x = 13
x = \(\frac{13}{2}\)
b) ( 6x - 12 ) . ( x + 5 ) = 0
\(\Rightarrow\orbr{\begin{cases}6x-12=0\\x+5=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2\\x=-5\end{cases}}\)
c) |2x - 1 | + 3 = 62
|2x - 1 | + 3 = 36
|2x - 1 | = 36 - 3
|2x - 1 | = 33
\(\Rightarrow\orbr{\begin{cases}2x-1=33\\2x-1=-33\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=17\\x=-16\end{cases}}\)
d) 4x - 3 = 2 . ( x + 2 ) - 17
4x - 3 = 2x + 4 - 17
4x - 2x = 4 - 17 + 3
2x = -10
x = -10 : 2
x = -5
a) 2x - 8 = 5
2x = 5 + 8
2x = 13
x = 13/2
vậy x = 13/2
b) ( 6x - 12 ).( x + 5 ) = 0
=> 6x - 12 = 0
x + 5 = 0
=> x = 2
x = -5
vậy x = 2; -5
c) | 2x - 1 | + 3 = 6^2
| 2x - 1 | + 3 = 36
| 2x - 1 | = 36 - 3
| 2x - 1 | = 33
* 2x - 1 = 33
2x = 34
x = 34 : 2
x = 17
* 2x - 1 = -33
2x = -33 + 1
2x = 32
x = 32 : 2
x = 16
vậy x thuộc {17; 16}
A , 3 - ( 17 - x ) = 289 - ( 36 + 289 )
3 - 17 + x = 0 - 36
-14 + x = -36
x = -36 - ( - 14 ) = -22
B, 25 - ( x + 5 ) = -415 - ( 15 - 415 )
25 - x - 5 = 0 - 15
20 - x = -15
x = 20 - ( - 15 ) = 35
C , 34 + ( 21 - x ) = ( 3747 - 30 ) - 3746
34 + 21 - x = 1 - 30
55 - x = -29
x = 55 - (-29 ) = 74
D , -2x - ( x -17 ) = 34 - ( -x + 25 )
- 2x - x + 17 = 34 - 25 + x
- 3x + 17 = 9 + x
- 3x - x = 9 - 17
-4x = -8
x = -8 : ( - 4 )
x = 2
E , 17x + ( -16x - 37 ) = x + 43
17x - 16x -37 = x + 43
x - 37 = x + 43
-37 - 43 = x - x
- 80 = 0 ( vô lý )
G , ( x + 12 ) . (x - 3 ) = 0
\(\hept{\begin{cases}x+12=0\\x-3=0\end{cases}}\)
\(\hept{\begin{cases}x=-12\\x=3\end{cases}}\)
a) \(\frac{3}{4}x-\frac{1}{4}=2\left(x-3\right)+\frac{1}{4}x\)
\(\frac{3}{4}x-\frac{1}{4}=2x-6+\frac{1}{4}x\)
\(\frac{3}{4}x-2x-\frac{1}{4}x=\frac{1}{4}-6\)
\(x\left(\frac{3}{4}-2-\frac{1}{4}\right)=-\frac{23}{4}\)
\(-\frac{3}{2}x=-\frac{23}{4}\)
\(x=-\frac{23}{4}\div\left(-\frac{3}{2}\right)\)
\(x=\frac{23}{6}\)
b) \(30\%-x+\frac{5}{6}=\frac{1}{3}\)
\(\frac{3}{10}-x+\frac{5}{6}=\frac{1}{3}\)
\(\frac{3}{10}-x=\frac{1}{3}-\frac{5}{6}\)
\(\frac{3}{10}-x=-\frac{1}{2}\)
\(x=\frac{3}{10}-\left(-\frac{1}{2}\right)\)
\(x=\frac{4}{5}\)