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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
a: \(4x^3+12=120\)
=>\(4x^3=108\)
=>\(x^3=27=3^3\)
=>x=3
b: \(\left(x-4\right)^2=64\)
=>\(\left[{}\begin{matrix}x-4=8\\x-4=-8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=12\\x=-4\end{matrix}\right.\)
c: (x+1)^3-2=5^2
=>\(\left(x+1\right)^3=25+2=27\)
=>x+1=3
=>x=2
d: 136-(x+5)^2=100
=>(x+5)^2=36
=>\(\left[{}\begin{matrix}x+5=6\\x+5=-6\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-11\end{matrix}\right.\)
e: \(4^x=16\)
=>\(4^x=4^2\)
=>x=2
f: \(7^x\cdot3-147=0\)
=>\(3\cdot7^x=147\)
=>\(7^x=49\)
=>x=2
g: \(2^{x+3}-15=17\)
=>\(2^{x+3}=32\)
=>x+3=5
=>x=2
h: \(5^{2x-4}\cdot4=10^2\)
=>\(5^{2x-4}=\dfrac{100}{4}=25\)
=>2x-4=2
=>2x=6
=>x=3
i: (32-4x)(7-x)=0
=>(4x-32)(x-7)=0
=>4(x-8)*(x-7)=0
=>(x-8)(x-7)=0
=>\(\left[{}\begin{matrix}x-8=0\\x-7=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=8\\x=7\end{matrix}\right.\)
k: (8-x)(10-2x)=0
=>(x-8)(x-5)=0
=>\(\left[{}\begin{matrix}x-8=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=5\end{matrix}\right.\)
m: \(3^x+3^{x+1}=108\)
=>\(3^x+3^x\cdot3=108\)
=>\(4\cdot3^x=108\)
=>\(3^x=27\)
=>x=3
n: \(5^{x+2}+5^{x+1}=750\)
=>\(5^x\cdot25+5^x\cdot5=750\)
=>\(5^x\cdot30=750\)
=>\(5^x=25\)
=>x=2
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
Câu 1:
a: =>-2x-x+17=34+x-25
=>-3x+17=x+9
=>-4x=-8
hay x=2
b: =>17x+16x+27=2x+43
=>33x+27=2x+43
=>31x=16
hay x=16/31
c: =>-2x-3x+51=34+2x-50
=>-5x+51=2x-16
=>-7x=-67
hay x=67/7
e: 3x-32>-5x+1
=>8x>33
hay x>33/8
a) x – 32 : 16 = 48 ó x – 2 = 48 ó x = 48 + 2 ó x = 50
b) 88 – 3.(7+x) = 64 ó 3.(7+x) = 88 – 64 ó 7 + x = 24:3 ó x = 8 – 7 ó x = 1
c) (5+4x) : 3 – 121 : 11 = 4 ó (5+4x) : 3 – 11 = 4 ó (5+4x) : 3 = 4 + 11 ó 5+4x = 15.3 ó 4x = 45 – 5 ó 4x = 40 ó x = 10
d) 15 – 2(3x+1) = 11.13 – 130 ó 15 – 2(3x+1) = 143 – 130 ó 15 – 2(3x+1) = 13
ó 2(3x+1) = 15 – 13 ó 3x + 1 = 2:2 ó 3x = 1 – 1 ó 3x = 0 ó x = 0
a) \(\left(x+2\right)^2-\left(3x-7\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=3x-7\\x+2=-3x+7\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3x=-2-7\\x+3x=-2+7\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-2x=-9\\4x=5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{2}\\x=\dfrac{5}{4}\end{matrix}\right.\)
Mấy câu kia tương tự.
a) \(\left(x+2\right)^2-\left(3x-7\right)^2=0\)
\(\Leftrightarrow\left(x+2-3x+7\right)\left(x+2+3x-7\right)=0\)
\(\Leftrightarrow\left(-2x+9\right)\left(4x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-2x+9=0\\4x-5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-2x=-9\\4x=5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-9}{-2}=\dfrac{9}{2}\\x=\dfrac{5}{4}\end{matrix}\right.\)
Vậy \(x=\dfrac{9}{2}\) hoặc \(x=\dfrac{5}{4}\)
b) lộn đề à
c) \(25\left(x-3\right)^2-49\left(2x+1\right)^2=0\)
\(\Leftrightarrow5^2\left(x-3\right)^2-7^2\left(2x+1\right)^2=0\)
\(\Leftrightarrow\left[5\left(x-3\right)\right]^2-\left[7\left(2x+1\right)\right]^2=0\)
\(\Leftrightarrow\left(5x-15\right)^2-\left(14x+7\right)^2=0\)
\(\Leftrightarrow\left(5x-15-14x-7\right)\left(5x-15+14x+7\right)=0\)
\(\Leftrightarrow\left(-9x-22\right)\left(19x-8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-9x-22=0\\19x-8=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-9x=22\\19x=8\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{22}{-9}=\dfrac{-22}{9}\\x=\dfrac{8}{19}\end{matrix}\right.\)
Vậy \(x=\dfrac{-22}{9}\) hoặc \(x=\dfrac{8}{19}\)
d) \(9\left(3x-2\right)^2=121\left(1-4x\right)^2\)
\(\Leftrightarrow9\left(3x-2\right)^2-121\left(1-4x\right)^2=0\)
\(\Leftrightarrow3^2\left(3x-2\right)^2-11^2\left(1-4x\right)^2=0\)
\(\Leftrightarrow\left[3\left(3x-2\right)\right]^2-\left[11\left(1-4x\right)\right]^2=0\)
\(\Leftrightarrow\left(9x-6\right)^2-\left(11-44x\right)^2=0\)
\(\Leftrightarrow\left(9x-6-11+44x\right)\left(9x-6+11-44x\right)=0\)
\(\Leftrightarrow\left(53x-17\right)\left(-35x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}53x-17=0\\-35x+5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}53x=17\\-35x=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{17}{53}\\x=\dfrac{-5}{-35}=\dfrac{1}{7}\end{matrix}\right.\)
Vậy \(x=\dfrac{17}{53}\) hoặc \(x=\dfrac{1}{7}\)
1) 5x = 120 : 2
5x = 60
x = 60 : 5
x = 12.
2) 3x + 27 = 45
3x = 45 - 27
3x = 18
x = 18 : 3
x = 6.
3) 73 + x - 122 = 234 : 2
73 + x - 122 = 117
73 + x = 117 + 122
73 + x = 239
x = 239 - 73
x = 166.
4) 32 - 2 ( x - 1 ) = 12
2 ( x - 1 ) = 32 - 12
2 ( x - 1 ) = 20
x - 1 = 20 : 2
x - 1 = 10
x = 10 + 1
x = 11.
5) 3 ( x + 1 ) - 15 = 36
3 ( x + 1 ) = 36 + 15
3 ( x + 1 ) = 51
x + 1 = 51 : 3
x + 1 = 17
x = 17 - 1
x = 16.
6) 32 - ( 4x - 16 ) = 21
4x - 16 = 32 - 21
4x - 16 = 11
4x = 11 + 16
4x = 27
x = 27 : 4
x = 6,75.
7) 13x - 3x = 500
( 13 - 3 )x = 500
10x = 500
x = 500 : 10
x = 50.
8) 9x + x - 35 = 68
9x + 1x - 35 = 68
9x + 1x = 68 + 35
9x + 1x = 103
( 9 + 1 )x = 103
10x = 103
x = 103 : 10
x = 10,3.
1) 5x = 120 : 2
5x = 60
x = 60 : 5
x = 12.
2) 3x + 27 = 45
3x = 45 - 27
3x = 18
x = 18 : 3
x = 6.
3) 73 + x - 122 = 234 : 2
73 + x - 122 = 117
73 + x = 117 + 122
73 + x = 239
x = 239 - 73
x = 166.
4) 32 - 2 ( x - 1 ) = 12
2 ( x - 1 ) = 32 - 12
2 ( x - 1 ) = 20
x - 1 = 20 : 2
x - 1 = 10
x = 10 + 1
x = 11.
5) 3 ( x + 1 ) - 15 = 36
3 ( x + 1 ) = 36 + 15
3 ( x + 1 ) = 51
x + 1 = 51 : 3
x + 1 = 17
x = 17 - 1
x = 16.
6) 32 - ( 4x - 16 ) = 21
4x - 16 = 32 - 21
4x - 16 = 11
4x = 11 + 16
4x = 27
x = 27 : 4
x = 6,75.
7) 13x - 3x = 500
( 13 - 3 )x = 500
10x = 500
x = 500 : 10
x = 50.
8) 9x + x - 35 = 68
9x + 1x - 35 = 68
9x + 1x = 68 + 35
9x + 1x = 103
( 9 + 1 )x = 103
10x = 103
x = 103 : 10
x = 10,3.
a) 7x - 5 = 16 b) 156 - 2x = 82 c) 10x + 65 = 125
=> 7x = 16 + 5 => 2x = 156 - 82 => 10x = 125 - 65
=> 7x = 21 => 2x = 74 => 10x = 60
=> x = 21 : 7 => x = 74 : 2 => x = 60 : 10
=> x = 3 => x = 37 => x = 6
Vậy x = 3 Vậy x = 37 Vậy x = 6
d) 8x + 2x = 25.2 e) 15 + 5x = 40 f) 5x + 2x = 6 - 5
=> 10x = 50 => 5x = 40 - 15 => 7x = 1
=> x = 50 : 10 => 5x = 25 => x = 1 : 7
=> x = 5 => x = 25 : 5 => x = 1/7
Vậy x = 5 => x = 5 Vậy x = 1/7
Vậy x = 5
g) 5x + x = 150 : 2 + 3 h) 6x + 3x = 5 : 5 + 3 i) 5x + 3x = 3 : 3 . 4 + 12
=> 6x = 75 + 3 => 9x = 1 + 3 => 8x = 1 . 4 + 12
=> 6x = 78 => 9x = 4 => 8x = 4 + 12
=> x = 78 : 6 => x = 4 : 9 => 8x = 16
=> x = 13 => x = 4/9 => x = 16 : 8
Vậy x = 13 Vậy x = 4/9 => x = 2
Vậy x = 2
j) 4x + 2x = 68 - 2 : 2 k) 5x + x = 39 - 3 : 3 l) 7x - x = 5 : 5 + 3 . 2 - 7
=> 6x = 68 - 1 => 6x = 39 - 1 => 6x = 1 + 6 - 7
=> 6x = 67 => 6x = 38 => 6x = 7 - 7
=> x = 67 : 6 => x = 38 : 6 => 6x = 0
=> x = 67/6 => x = 19/3 => x = 0
Vậy x = 67/6 Vậy x = 19/3 Vậy x = 0
m) 7x - 2x = 6 : 6 + 44 : 11
=> 5x = 1 + 4
=> 5x = 5
=> x = 5 : 5
=> x = 1
Vậy x = 1
Mỏi tay ~~~~~~~~~~~~~~
17x + 3. ( -16x – 37) = 2x + 43 - 4x
<=>17x-48x-111=-2x+43
<=>-29x=154
<=> \(x=-\frac{154}{29}\)
-3. (2x + 5) -16 < -4. (3 – 2x)
\(\Leftrightarrow-6x-31< -12+8x.\)
\(\Leftrightarrow-14x< 19\Rightarrow x< -\frac{19}{14}\)
\(a,\left(x-2\right)^2=64\)
\(\Rightarrow x-2=\orbr{\begin{cases}8\\-8\end{cases}}\)
\(\Rightarrow x=\orbr{\begin{cases}10\\-6\end{cases}}\)
\(b,\left(5x-1\right)^3=64\)
\(\Rightarrow5x-1=4\)
\(\Rightarrow5x=5\Leftrightarrow x=1\)
\(c,3^x+3^{x+3}=270\)(đề sai)
\(d,4^{x+1}+4^{x+2}=336\)(đề sai)
\(e,S=1+3+3^2+...+3^{50}\)
\(\Rightarrow2S=3^{51}-1\)
\(\Rightarrow S=\frac{3^{51}-1}{2}\)
a) \(\left(x-2\right)^2=64\)
\(\Rightarrow\orbr{\begin{cases}\left(x-2\right)^2=8^2\\\left(x-2\right)^2=\left(-8\right)^2\end{cases}}\Rightarrow\orbr{\begin{cases}x-2=8\\x-2=-8\end{cases}}\Rightarrow\orbr{\begin{cases}x=10\\x=-6\end{cases}}\)
Vậy x = 10 hoặc x = -6
b) \(\left(5x-1\right)^3=64\)
\(\Rightarrow\left(5x-1\right)^3=4^3\)
\(\Rightarrow5x-1=4\)
\(\Rightarrow5x=4+1\)
\(\Rightarrow5x=5\)
\(\Rightarrow x=5:5\)
\(\Rightarrow x=1\)
Vậy x = 1
c) \(3^x+3^{x+3}=270\)
\(\Rightarrow3^x+3^x\times3^3=270\)
\(\Rightarrow3^x\times\left(1+3^3\right)=270\)
\(\Rightarrow3^x\times28=270\)
\(\Rightarrow3^x=270:28\)
\(\Rightarrow3^x=\frac{135}{14}\)
\(\Rightarrow\)Không có giá trị x thỏa mãn
Vậy không có giá trị x thỏa mãn
d) \(S=1+3+3^2+...+3^{50}\)
\(\Rightarrow3S=3+3^2+3^3+...+3^{51}\)
\(\Rightarrow3S-S=\left(3+3^2+3^3+...+3^{51}\right)-\left(1+3+3^2+...+3^{50}\right)\)
\(\Rightarrow2S=3^{51}-1\)
\(\Rightarrow S=\frac{3^{51}-1}{2}\)
Vậy \(S=\frac{3^{51}-1}{2}\)
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