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1.
2|x-6|+7x-2=|x-6|+7x
2|x-6| - |x-6|=7x-(7x-2)
|x-6| = 2
=>x-6 = +2
*x-6=2 *x-6 = -2
x =2+6 x = (-2)+6
x =8 x = 4
2.
|x-5|-7(x+4)=5-7x
|x-5|-7x-28 =5-7x
|x-5|-28 =5-7x+7x
|x-5|-28 = 5
|x-5| = 5+28
|x-5| = 33
=>x-5 = +33
*x-5=33 *x-5=-33
x =38 x = -28
3.
3|x+4|-2(x-1)=7-2x
3|x+4|-2x+2 =7-2x
3|x+4|-2 =7-2x+2x
3|x+4|-2 =7
3|x+4| =7+2
3|x+4| = 9
|x+4| =9:3
|x+4| = 3
=>x+4 = +3
*x+4=3 *x+4=-3
x =-1 x = -7
a)=1/2 . 8/15 - 3/4.47/9
=4/15 - 47/12
=-73/20
b)=2-1/3 . -21/20
=2+7/20
=47/20
1,
( 2x-5) + 17=6
\(2x-5=6-17\)
\(2x-5=-11\)
\(2x=-11+5\)
\(2x=-6\)
\(x=-6:2\)
\(x=-3\)
Vậy \(x=3\)
2,
10-2(4-3x)=-4
\(-2\left(4-3x\right)=-4-10\)
\(-2\left(4-3x\right)=-14\)
\(4-3x=-14:\left(-2\right)\)
\(4-3x=7\)
\(-3x=7-4\)
\(-3x=3\)
\(x=3:\left(-3\right)\)
\(x=-1\)
Vậy \(x=-1\)
3,
-12+3(-x+7)=-18
\(3\left(-x+7\right)=-18+12\)
\(3\left(-x+7\right)=-6\)
\(-x+7=-6:3\)
\(-x+7=-2\)
\(-x=-2-7\)
\(-x=-9\)
\(x=9\)
\(\text{Vậy }x=9\)
4,
24:(3x -2)=-3
\(3x-2=24:\left(-3\right)\)
\(3x-2=-8\)
\(3x=-8+2\)
\(3x=-6\)
\(x=-6:3\)
\(x=-2\)
\(\text{Vậy }x=-2\)
5,
-45:5.(-3-2x)=3
\(5\left(-3-2x\right)=-45:3\)
\(5\left(-3-2x\right)=-15\)
\(-3-2x=-15:5\)
\(-3-2x=-3\)
\(-2x=-3+3\)
\(-2x=0\)
\(x=0\)
Vậy \(x=0\)
6,
x.(x+7)= 0
\(\Rightarrow\left\{{}\begin{matrix}x=0\\x+7=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=0\\x=-7\end{matrix}\right.\)
\(\text{Vậy}\left\{{}\begin{matrix}x=0\\x=-7\end{matrix}\right.\)
7,
( x+ 12 ) .( x-3)=0
\(\Rightarrow\left\{{}\begin{matrix}x+12=0\\x-3=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=-12\\x=3\end{matrix}\right.\)
\(\text{Vậy }\left\{{}\begin{matrix}x=-12\\x=3\end{matrix}\right.\)
8,
(-x+5).(3-x) =0
\(\Rightarrow\left\{{}\begin{matrix}-x+5=0\\3-x=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}-x=-5\\-x=-3\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=5\\x=3\end{matrix}\right.\)
Vậy \(x=5\text{ hoặc }x=3\)
9, x.( 2+x).(7-x)=0
\(\Rightarrow\left\{{}\begin{matrix}x=0\\2+x=0\\7-x=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=0\\x=-2\\x=7\end{matrix}\right.\)
Vậy \(\left\{{}\begin{matrix}x=0\\x=-2\\x=7\end{matrix}\right.\)
10,
(x-1).(x+2).(-x-3)=0
\(\Rightarrow\left\{{}\begin{matrix}x-1=0\\x+2=0\\-x-3=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=1\\x=-2\\-x=3\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=1\\x=-2\\x=-3\end{matrix}\right.\)
Vậy \(\left\{{}\begin{matrix}x=1\\x=-2\\x=-3\end{matrix}\right.\)
a) \(\dfrac{1}{2}-\left(x+\dfrac{1}{3}\right)=\dfrac{5}{6}\)
\(\Rightarrow x+\dfrac{1}{3}=\dfrac{1}{2}-\dfrac{5}{6}\)
\(\Rightarrow x+\dfrac{1}{3}=\dfrac{-1}{3}\)
\(\Rightarrow x=\dfrac{-1}{3}-\dfrac{1}{3}\)
\(\Rightarrow x=\dfrac{-2}{3}\)
b)\(\dfrac{3}{4}-\left(x+\dfrac{1}{2}\right)=\dfrac{4}{5}\)
\(\Rightarrow x+\dfrac{1}{2}=\dfrac{3}{4}-\dfrac{4}{5}\)
\(\Rightarrow x+\dfrac{1}{2}=\dfrac{-1}{20}\)
\(\Rightarrow x=\dfrac{-1}{20}-\dfrac{1}{2}\)
\(\Rightarrow x=\dfrac{-11}{20}\)
c) \(\dfrac{3}{35}-\left(\dfrac{3}{5}+x\right)=\dfrac{2}{7}\)
\(\Rightarrow\dfrac{3}{5}+x=\dfrac{3}{35}-\dfrac{2}{7}\)
\(\Rightarrow\dfrac{3}{5}+x=\dfrac{-1}{5}\)
\(\Rightarrow x=\dfrac{-1}{5}-\dfrac{3}{5}\)
\(\Rightarrow x=\dfrac{-4}{5}\)
d)\(\dfrac{2}{3}.x=\dfrac{4}{27}\)
\(\Rightarrow x=\dfrac{4}{27}:\dfrac{2}{3}\)
\(\Rightarrow x=\dfrac{2}{9}\)
e) \(\dfrac{-3}{5}.x=\dfrac{21}{10}\)
\(\Rightarrow x=\dfrac{21}{10}:\dfrac{-3}{5}\)
\(\Rightarrow x=\dfrac{-7}{2}\)
a) ( 3x - 4 ) . ( x - 1 ) 3 = 0
\(\Rightarrow\orbr{\begin{cases}3x-4=0\\\left(x-1\right)^3=0\end{cases}}\Rightarrow\orbr{\begin{cases}3x=4\\x-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{4}{3}\\x=1\end{cases}}\)
b) x17 = x
\(\Rightarrow\)x17 - x = 0
\(\Rightarrow\)x . ( x16 - 1 ) = 0
\(\Rightarrow\orbr{\begin{cases}x=0\\x^{16}-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x^{16}=1\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
c) 22x - 1 : 4 = 83
22x - 1 : 22 = 29
22x - 1 = 29 . 22
22x - 1 = 211
\(\Rightarrow\)2x - 1 = 11
\(\Rightarrow\)2x = 12
\(\Rightarrow\)x = 6
d) ( x + 2 ) 5 = 210
( x + 2 ) 5 = 45
\(\Rightarrow\)x + 2 = 4
\(\Rightarrow\)x = 4 - 2 = 2
e) ( x - 5 ) 4 = ( x - 5 ) 6
( x - 5 ) 4 - ( x - 5 ) 6 = 0
( x - 5 ) 4 . [ 1 - ( x - 5 ) 2 ] = 0
\(\Rightarrow\orbr{\begin{cases}\left(x-5\right)^4=0\\1-\left(x-5\right)^2=0\end{cases}}\Rightarrow\orbr{\begin{cases}x-5=0\\\left(x-5\right)^2=1\end{cases}}\Rightarrow\orbr{\begin{cases}x=5\\x-5=1\end{cases}}\Rightarrow\orbr{\begin{cases}x=5\\x=6\end{cases}}\)
f ) số số hạng của dãy trên là :
( x - 1 ) : 1 + 1 = x ( số )
tổng của dãy trên là :
( x + 1 ) . x : 2 = 78
( x + 1 ) . x = 78 . 2 = 156
Phân tích : 156 = 22 . 3 . 13 = ( 22 . 3 ) . 13 = 12 . 13
\(\Rightarrow\)x = 12
g) ( x + 1 ) 2 = ( x + 1 ) 0
( x + 1 ) 2 = 1
\(\Rightarrow\)x + 1 = 1
\(\Rightarrow\)x = 1 - 1 = 0
h) ( 2 + x ) + ( 4 + x ) + ( 6 + x ) + ... + ( 52 + x ) = 780
( 2 + 4 + 6 + ... + 52 ) + ( x + x + x + ... + x ) = 780
2 . ( 1 + 2 + 3 + ... + 26 ) + 26x = 780
2 . 351 + 26x = 780
702 + 26x = 780
26x = 780 - 702
26x = 78
x = 78 : 26
x = 3
a) (3x - 4) . (x - 1)3 = 0
+) (3x - 4) =0
3x =0+4
3x =4
x =3:4
x =0,75