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\(\left(x+\dfrac{2}{3}\right)+\dfrac{1}{11}=\left(\dfrac{10}{-33}.\dfrac{11}{8}\right).\dfrac{24}{-55}\)
\(\Rightarrow\left(x+\dfrac{2}{3}\right)+\dfrac{1}{11}=\dfrac{-5}{12}.\dfrac{24}{-55}\)
\(\Rightarrow\left(x+\dfrac{2}{3}\right)+\dfrac{1}{11}=\dfrac{2}{11}\)
\(\Rightarrow x+\dfrac{2}{3}=\dfrac{2}{11}-\dfrac{1}{11}\)
\(\Rightarrow x+\dfrac{2}{3}=\dfrac{1}{11}\)
\(\Rightarrow x=\dfrac{1}{11}-\dfrac{2}{3}\)
\(\Rightarrow x=-\dfrac{19}{33}\)
\(\dfrac{48}{25}\cdot\dfrac{27}{55}+2\dfrac{4}{9}\cdot\dfrac{14}{33}\)
\(=\dfrac{1296}{1375}+\dfrac{22}{9}\cdot\dfrac{14}{33}\\ =\dfrac{1296}{1375}+\dfrac{28}{27}\\ =\dfrac{34992}{37125}+\dfrac{38500}{37125}\\ =\dfrac{73492}{37125}\)
\(1\dfrac{19}{22}\cdot\left(\dfrac{47}{77}-\dfrac{16}{15}\right)\\ =\dfrac{41}{22}\cdot\dfrac{-527}{1155}\\ =\dfrac{-21607}{25410}\)
\(\left(3\dfrac{10}{99}+4\dfrac{11}{99}-5\dfrac{8}{299}\right)-\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)\\ =\left(\dfrac{307}{99}+\dfrac{37}{99}-\dfrac{1503}{299}\right)-0\\ =\dfrac{344}{99}-\dfrac{1053}{299}\\ =-\dfrac{107}{2277}\)
Bài 3
\(\dfrac{55}{23}+\dfrac{-22}{23}\le x\le\dfrac{1}{5}-\dfrac{-1}{6}+\dfrac{79}{30}\)
\(=\dfrac{33}{23}\)\(\le x\le\dfrac{90}{30}\)
\(=\dfrac{33}{23}\le x\le3\)
Mà \(x\in Z\) \(\Rightarrow\)\(x=2\)
Có 1 giá trị thỏa mãn
Chọn A
Bài 4
\(\dfrac{-11}{12}< \dfrac{5}{x}< \dfrac{-11}{15}\)
Chọn D
Bài 5
\(M=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{99\cdot100}\)
\(M=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{100}\)
\(M=1-\dfrac{1}{100}\)
\(M=\dfrac{100}{100}-\dfrac{1}{100}\)
\(M=\dfrac{99}{100}\)
CHọn C
-( -x + 13 - 142 ) + 18 = 55
-( -x - 129) + 18 = 55
x + 129 + 18 = 55
x + 147 = 55
x = 55 - 147
x = -92
b, 25 - 3.(6 -x ) = 22
3(6-x) = 25 - 22
3(6-x) = 3
6 - x = 1
x =5
c, [ ( 2x - 11 ) :3 +1] .5 = 20
( 2x - 11) : 3 + 1 = 20 : 5
(2x - 11) : 3 + 1 = 4
( 2x - 11) : 3 = 4 - 1
(2x - 11 ) : 3 = 3
2x - 11 = 3 x 3
2x - 11 = 9
2x = 9 + 11
2x = 20
x = 10
d, 3(x+5) - x - 11 = 24
3(x+5) - x = 24 +11
3x + 15 - x = 35
2x = 35 - 15
2x = 20
x = 10
Bài 2:
a: \(17-x=3\)
=>\(x=17-3\)
=>x=14(nhận)
b: \(2\cdot\left(x-1\right):3=6\)
=>\(2\left(x-1\right)=6\cdot3=18\)
=>x-1=18/2=9
=>x=9+1=10(nhận)
c: \(x+\left(-2\right)=\left(-11\right)+7\)
=>\(x-2=-4\)
=>\(x=-4+2=-2\left(loại\right)\)
d: \(\left(x-1\right)^2-5=20\)
=>\(\left(x-1\right)^2=25\)
=>\(\left[{}\begin{matrix}x-1=5\\x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\left(nhận\right)\\x=-4\left(loại\right)\end{matrix}\right.\)
Câu 3:
a: Đặt *=a
\(\overline{57a3}⋮9\)
=>\(5+7+a+3⋮9\)
=>\(a+15⋮3\)
mà 0<=a<=9
nên a=3
=>*=a
b: \(A=123\cdot7+8+9\)
123*7 là số lẻ
9 là số lẻ
=>123*7+9 chia hết cho 2
mà 8 chia hết cho 2
nên \(A=123\cdot7+9+8⋮2\)
\(123\cdot7⋮3;9⋮3;8⋮̸3\)
=>\(A=123\cdot7+9+8⋮̸3\)
c: \(B=3\cdot5\cdot7+10^{50}\)
\(=5\cdot3\cdot7+5\cdot5^{49}\cdot2^{49}\)
\(=5\left(3\cdot7+5^{49}\cdot2^{49}\right)⋮5\)
=>B là hợp số
a)23+3 𝑥 =125 | b) 70 – 5.(𝑥 - 3)= 45 | c) 20 + 5 𝑥 = 57:55
3 𝑥 +23=125 | 70−5 𝑥 +15=45 | 5 𝑥 +20=5755
𝑥=34 | 𝑥=8 | 𝑥=−104
275
|x - 22| - 33 = -20
|x - 22| = -20 + 33
|x - 22| = 13
x = 13 + 22
x = 35
còn một cách khác nhưng mik ko biết
! x - 22 ! = -20 + 33
! x - 22 ! = 13
x - 22 = 13 hay x - 22 = -13
x = 13 + 22 hay x = -13 + 22
x = 35 hay x = 9
\(5^5.\dfrac{1}{20}.2^2.3^3:125\)
\(=5^5.\dfrac{1}{2^2.5}.2^2.3^3:5^3\)
\(=\dfrac{2^2.3^3.5^5}{2^2.5^4}=3^3.5=27.5=135\)
= 3125 x 1/20 x 4 x 27 : 125
= 625/4 x 4 x 27 : 125
= 625 x 27 : 125
= 16875 : 125
= 135