52-2x=-11
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(C) có tâm I(−1;2), bán kính R = 4. (C’) có tâm I′(10; −5), bán kính R’ = 4. Vậy ( C ′ ) = T v → ( C ) , v → = I I ' → = ( 11 ; − 7 ) .
a) 2x + 15 = 45
2x = 45 - 15
2x = 30
x = 30 : 2
x = 15 (nhận)
Vậy x = 15
b) 120 - 2.(x + 3) = 22.52
120 - 2.(x + 3) = 1144
2.(x + 3) = 120 - 1144
2.(x + 3) = - 1024
x + 3 = -1024 : 2
x + 3 = -512
x = - 512 - 3
x = -515 (loại)
Vậy không tìm được x thỏa mãn x là số tự nhiên
c) 11 ⋮ (x - 2)
⇒ x - 2 ∈ Ư(11) = {-11; -1; 1; 11}
⇒ x ∈ {-9; 1; 3; 13}
Do x là số tự nhiên
⇒ x ∈ {1; 3; 13}
d) Do 12 ⋮ x và 18 ⋮ x nên x ∈ ƯC(12; 18)
12 = 2².3
18 = 2.3²
ƯCLN(12; 18) = 2.3 = 6
⇒ x ∈ ƯC(12; 18) = {1; ; 3; 6}
1)
a) 2x + 5 = 3⁴ : 3²
2x + 5 = 3²
2x + 5 = 9
2x = 9 - 5
2x = 4
x = 4 : 2
x = 2
b) (3x - 24).73 = 2.74
(3x - 24).73 = 148
3x - 24 = 148/73
3x = 148/73 + 24
3x = 1900/73
x = 1900/73 : 3
x = 1900/219
c) [3.(42 - x)] + 15 = 23.3
126 - 3x + 15 = 69
141 - 3x = 69
3x = 141 - 69
3x = 72
x = 72 : 3
x = 24
d) 126 + (132 - x) = 300
132 - x = 300 - 126
132 - x = 174
x = 132 - 174
x = -42
2)
a) 120 - (x + 55) = 60
x + 55 = 120 - 60
x + 155 = 60
x = 60 - 55
x = 5
b) (7x - 11).3 = 25.52 + 200
(7x - 11).3 = 1500
7x - 11 = 1500 : 3
7x - 11 = 500
7x = 500 + 11
7x = 511
x = 511 : 7
x = 73
c) 2x + 2x + 4 = 544
4x = 544 - 4
4x = 540
x = 540 : 4
x = 135
\(1,\\ \left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\\ \Leftrightarrow\left(x-7\right)^{x+1}\left[1-\left(x-7\right)^{10}\right]=0\\ \Leftrightarrow\left[{}\begin{matrix}\left(x-7\right)^{x+1}=0\\\left(x-7\right)^{10}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-7=0\\x-7=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=8\end{matrix}\right.\)
\(2,\\ a,\left|2x-3\right|>5\Leftrightarrow\left[{}\begin{matrix}2x-3< -5\\2x-3>5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x< -1\\x>4\end{matrix}\right.\\ b,\left|3x-1\right|\le7\Leftrightarrow\left[{}\begin{matrix}3x-1\le7\\1-3x\le7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\le\dfrac{8}{3}\\x\ge-2\end{matrix}\right.\\ c,\cdot x< -\dfrac{3}{2}\\ \Leftrightarrow5-3x+\left(-2x-3\right)=7\Leftrightarrow2-5x=7\Leftrightarrow x=-1\left(ktm\right)\\ \cdot-\dfrac{3}{2}\le x\le\dfrac{5}{3}\\ \Leftrightarrow\left(5-3x\right)+\left(2x+3\right)=7\Leftrightarrow8-x=7\Leftrightarrow x=1\left(tm\right)\\ \cdot x>\dfrac{5}{3}\\ \Leftrightarrow\left(3x-5\right)+\left(2x+3\right)=7\Leftrightarrow5x-2=7\Leftrightarrow x=\dfrac{9}{5}\left(tm\right)\\ \Leftrightarrow S=\left\{1;\dfrac{9}{5}\right\}\)
a) \(\left(-48\right)+127+\left(-52\right)+73\)
\(=\left(-48-52\right)+\left(127+73\right)\)
\(=-100+200\)
\(=100\)
b) \(\left(-38\right)\cdot45+\left(-38\right)\cdot55\)
\(=\left(-38\right)\cdot\left(45+55\right)\)
\(=\left(-38\right)\cdot100\)
\(=-3800\)
c) \(\left(-125\right)+371+\left(-875\right)+629+150\)
\(=\left(-125-875\right)+\left(371+629\right)+150\)
\(=-1000+1000+150\)
\(=150\)
d) \(271+\left(-392\right)+729+\left(-608\right)+\left(-123\right)\)
\(=\left(271+729\right)+\left(-392-608\right)-123\)
\(=1000-1000-123\)
\(=-123\)
e) \(\left(-48\right)\cdot25+25\cdot\left(-52\right)\)
\(=25\cdot\left(-48-52\right)\)
\(=25\cdot-100\)
\(=-2500\)
f) \(47\cdot\left(-11\right)+47\)
\(=47\cdot\left(-11+1\right)\)
\(=47\cdot-10\)
\(=-470\)
g) \(56-7\cdot8+11\)
\(=56-56+11\)
\(=0+11\)
\(=11\)
h) \(-42+51+2+\left(-11\right)+40\)
\(=\left(-42+2\right)+\left(51-11\right)+40\)
\(=-40+40+40\)
\(=0+40\)
\(=40\)
a: =-48-52+127+73
=200-100
=100
b; \(=-38\left(45+55\right)=-38\cdot100=-3800\)
c: \(=-125-875+371+629+150\)
=-1000+1000+150
=150
d: =271+729-392-608-123
=1000-1000-123
=-123
e: =25(-48-52)
=25*(-100)
=-2500
f: =47(-11+1)
=47(-10)
=-470
g: =56-56+11
=11
h: =-42+2+51-11+40
=-40+40+40
=40
a) \(\frac{x+3}{11}=\frac{1}{2}\Rightarrow x+3=5,5\Rightarrow x=2,5\)
b)\(\frac{2x+11}{11}=18\Rightarrow2x+11=18.11=198\Rightarrow x=\frac{198-11}{2}=93,5\)
c) \(\frac{3x+52}{15}=\frac{21}{4}\Rightarrow3x+52=\frac{21}{4}.15=78,75\Rightarrow x=\frac{78,75-52}{3}=\frac{107}{12}\)
d) \(\frac{3x+1}{15}=\frac{2x-3}{4}\Rightarrow12x+4=30x-45\Rightarrow49=18x\Rightarrow x=\frac{49}{18}\)
e)\(\frac{2x+11}{44}=\frac{x+11}{10}\Rightarrow20x+110=44x+484\Rightarrow0=24x+374\Rightarrow x=\frac{-187}{12}\)
f)\(\frac{11x-32}{4}=17x+55-9x=8x+55\Rightarrow11x-32=32x+220\Rightarrow0=21x+252\Rightarrow x=-12\)
m) \(\frac{12x+11}{13}=\frac{8x}{7}\Rightarrow84x+77=104x\Rightarrow77=20x\Rightarrow x=\frac{77}{20}\)
Đáp án
𝑥=63
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2