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2: 12-10x=25-30x
=>20x=13
=>x=13/20
3: \(3\left(2x+3\right)-2\left(4x-5\right)=10x+21\)
=>6x+9-8x+10=10x+21
=>10x+21=-2x+19
=>12x=-2
=>x=-1/6
4: \(\Leftrightarrow25x-15-6x+12=11-5x\)
=>19x-3=11-5x
=>24x=14
=>x=7/12
5: \(\Leftrightarrow8-12x-5+10x=4-6x\)
=>4-6x=-2x+3
=>-4x=-1
=>x=1/4
6: \(\Leftrightarrow32x-24-6+9x=13-40x\)
=>41x-30=13-40x
=>81x=43
=>x=43/81
7: \(\Leftrightarrow10x-5+20x=5x-11\)
=>30x-5=5x-11
=>25x=-6
=>x=-6/25
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c) x.(1+2+3+4+...+100)=0
x.5050=0
x=0:5050=0
Vậy x=0
d) x.(1+2+3+4+5+...+100)=5050
x.5050=5050
x=1
Vậy x=1
e) x+1+x+2+x+3+x+4+...+x+100=5050
(x+x+x+x+...+x)+(1+2+3+4+...+100)=5050
100 số hạng x
x.100+5050=5050
x.100=0
x=0
Vậy x=0
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#)Giải :
b) Với : x < -6 , phương trình có dạng :
- x - 6 = 2x + 9
<=> -3x = 15
<=> x = - 5 ( không thỏa mãn )
Với : x ≥ - 6 , phương trình có dạng :
x + 6 = 2x + 9
<=> x = - 3 ( thỏa mãn)
Vậy , phương trình nhận : x = - 3 làm nghiệm duy nhất
#~Will~be~Pens~#
A, \(\left|9+6x\right|=2x\Rightarrow\orbr{\begin{cases}9+6x=2x\\9+6x=-2x\end{cases}\Rightarrow\orbr{\begin{cases}2x-6x=9\\-2x-6x=9\end{cases}}}\Rightarrow\orbr{\begin{cases}-4x=9\\-8x=9\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{-4}{9}\\x=\frac{-8}{9}\end{cases}}\)
B, \(\left|x+6\right|=2x+9\Rightarrow\orbr{\begin{cases}x+6=2x+9\\x+6=-2x-9\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-2x=9-6\\x+2x=-9-6\end{cases}}\Rightarrow\orbr{\begin{cases}-x=3\\3x=-15\end{cases}}\Rightarrow\orbr{\begin{cases}x=-3\\x=-5\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1.
a, \(x-14=3x+18\)
\(\Rightarrow x-3x=18+14\)
\(\Rightarrow-2x=32\Rightarrow x=\frac{32}{-2}=-16\)
b, \(\left(x+7\right).\left(x-9\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+7=0\\x-9=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-7\\x=9\end{cases}}}\)
c, \(\left|2x-5\right|-7=22\)
\(\Rightarrow\left|2x-5\right|=22+7\)
\(\Rightarrow\left|2x-5\right|=29\)
\(\Rightarrow\orbr{\begin{cases}2x+5=29\\2x-5=29\end{cases}}\Rightarrow\orbr{\begin{cases}2x=24\\2x=34\end{cases}\Rightarrow}\orbr{\begin{cases}x=12\\x=17\end{cases}}\)
d, \(\left(\left|2x\right|-5\right)-7=22\)
\(\Rightarrow\left(\left|2x\right|-5\right)=29\)
\(\Rightarrow\left|2x\right|=29+5\Rightarrow\left|2x\right|=34\Rightarrow x=\pm17\)
e, \(\left|x+3\right|+\left|x+9\right|+\left|x+5\right|=4x\)
Vì \(\left|x+3\right|\ge0;\left|x+9\right|\ge0;\left|x+5\right|\ge0;4x\ge0\)
Nên \(\left|x+3\right|+\left|x+9\right|+\left|x+5\right|=4x\ge0\)
\(\Rightarrow\left|x+3\right|>0\Rightarrow\left|x+3\right|=x+3\)
\(\left|x+9\right|>0\Rightarrow\left|x+9\right|=x+9\)
\(\left|x+5\right|>0\Rightarrow\left|x+5\right|=x+5\)
Ta có :
\(x+3+x+9+x+5=4x\)
\(\Rightarrow3x+\left(3+9+5\right)=4x\)
\(\Rightarrow4x-3x=17\)
\(\Rightarrow x=17\)
2. a , b sai đề bn
c, \(\left(5x+1\right).\left(y-1\right)=4\)
\(\Rightarrow\left(5x+1\right).\left(y-1\right)\inƯ\left(4\right)\)
\(\text{ }Ư\left(4\right)=\left\{1;-1;2;-2;4;-4\right\}\)
Ta có bảng sau :
5x+1 | 1 | -1 | 2 | -2 | 4 | -4 |
y-1 | -4 | 4 | -2 | 2 | -1 | 1 |
x | 0 | -2/5 | 1/5 | -3/5 | 3/5 | -1 |
y | -3 | 5 | -1 | 3 | 0 | 2 |
d, \(5xy-5x+y=5\)
\(\Rightarrow\left(5xy-5x\right)+y=5\)
\(\Rightarrow5x.\left(y-1\right)+y=5\)
\(\Rightarrow\left(5x+1\right).\left(y-1\right)=4\)
\(\Rightarrow\left(5x+1\right).\left(y-1\right)\inƯ\left(4\right)\)
\(Ư\left(4\right)=\left\{1;-1;2;-2;4;-4\right\}\)
Ta có bảng sau :
5x+1 | 1 | -1 | 2 | -2 | 4 | -4 |
y-1 | -4 | 4 | -2 | 2 | -1 | 1 |
x | 0 | -2 | 1/5 | -3/5 | 3/5 | -1 |
y | -3 | 5 | -1 | 3 | 0 | 2 |
![](https://rs.olm.vn/images/avt/0.png?1311)
A=-(3x+7)+(5x-2)+(2x-10)
=-3x-7+5x-2+2x-10
=(-3x+5x+2x)-(7+2+10)
=4x-19
B = (6x+8)-(4x-5)-3x
= 6x+8-4x+5-3x
= (6x-4x-3x) + (8+5)
= -x + 13
= 13-x
C = 2(5x+3) - (2x-1) + 12
= 10x+6 - 2x + 1 + 12
= (10x-2x) + (6+1+12)
= 8x + 19
D = (x+7)-3(x+1)+2x-5
= x+7-3x-3+2x-5
= (x-3x+2x) + (7-3-5)
= -1
![](https://rs.olm.vn/images/avt/0.png?1311)
a: 3x=81
nên x=27
b: \(5\cdot4^x=80\)
\(\Leftrightarrow4^x=16\)
hay x=2
c: \(2^x=4^5:4^3\)
\(\Leftrightarrow2^x=2^4\)
hay x=4
b) \(-2x+\left(-3x\right)+\left(-4x\right)+......+\left(-20x\right)=1254\)
\(\Rightarrow x.\left(-2-3-4-.......-20\right)=1254\)
\(\Rightarrow x.\left[-\left(2+3+4+.....+20\right)\right]=1254\)
\(\Rightarrow x.\left(-209\right)=1254\)
\(\Rightarrow x=1254:\left(-209\right)\)
\(\Rightarrow x=-6\)
c) \(\left|2x\right|=4\)
\(\Rightarrow\orbr{\begin{cases}2x=4\\2x=-4\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2\\x=-2\end{cases}}\)
d) \(\left|2x-1\right|=3\)
\(\Rightarrow\orbr{\begin{cases}2x-1=3\\2x-1=-3\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}2x=4\\2x=-2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2\\x=-1\end{cases}}\)
Cảm ơn nha ~