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a) \(\frac{1}{2}-\left(\frac{1}{3}+\frac{1}{4}\right)< x< \frac{1}{48}-\left(\frac{1}{16}-\frac{1}{6}\right)\)
=) \(\frac{-1}{12}< x< \frac{1}{8}\)
Vì \(\frac{-1}{12}< 0;\frac{1}{8}>0\)và \(< 1\)
mà x là số nguyên =) \(x=0\)
b) \(\frac{3}{4}-\frac{5}{6}\le\frac{x}{12}< 1-\left(\frac{2}{3}-\frac{1}{4}\right)\)
=) \(\frac{-1}{12}\le\frac{x}{12}< \frac{7}{12}\)
=) \(-1\le x< 7\)=) \(x=\left\{-1;0;1;2...;6\right\}\)

Ta có:
(1/2 + 1/4 + 1/8 + 1/16) = 8/16 + 4/16 + 2/16 + 1/16 = 15/16.
1/2 + 1/6 + 1/12 + 1/20 +…+ 1/132 = 1/(1.2) + 1/(2.3) + 1/(3.4) + 1/(4.5) +…+1/(11.12)
= (1 – 1/2) + (1/2 – 1/3) + (1/3 – 1/4) + (1/4 – 1/5) +…+ (1/11 – 1/12)
= 1 – 1/12 = 11/12
Vậy x = (15/16) : (11/12) = 45/44.
(1/2+1/4+1/8+1/16):x=1/2+1/6+1/12+1/20+...+1/132
(1-1/2+1/2-1/4+1/4-1/8+1/8-1/16):x=1/1x2+1/2x3+1/3x4+1/4x5+...+1/11x12
(1-1/16):x=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/11-1/12
15/16:x=1-1/12
15/16:x=11/12
x=15/16:11/12
x=45/44

1/2+1/4+1/6+1/8+1/16):x=3/1*2+3/2*3+3/3*4+...+3/15*16
\(\frac{53}{48}:x=3(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{15.16})\)
\(\frac{53}{48}:x=3(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{15}-\frac{1}{16})\)
\(\frac{53}{48}:x=3(1-\frac{1}{16})\)
\(\frac{53}{48}:x=\frac{45}{16}\)
\(x=\frac{53}{48}:\frac{45}{16}\)
\(x=\frac{53}{135}\)
Chúc bạn học tốt


Tìm số nguyên x, biết:
1) -16 + 23 + x = - 16
7+x=-16
x=-16-7
x=-23
2) 2x – 35 = 15
2x=15+35
2x=50
x=50:2
x=25
3) 3x + 17 = 12
3x=12-17
3x=-5
x=-5/3
4) (2x – 5) + 17 = 6
2x-5=6-17
2x-5=-11
2x=-11+5
2x=-6
x=-6:2
x=-3
5) 10 – 2(4 – 3x) = -4
2(4-3x)=10-(-4)
2(4-3x)=14
4-3x=14:2
4-3x=7
3x=4-7
3x=-3
x=-3:3
x=-1
6) - 12 + 3(-x + 7) = -18
3(-x+7)=-18-(-12)
3(x+7)=-6
x+7=-6:3
x+7=-2
x=-2-7
x=-9

3/2+5/4+9/8/+17/16+33/32-6+x-1/x+1=31/32-2/2015
=(1+1/2)+(1+1/4)+(1+1/8)+(1+1/16)+(1+1/32-6+x-1/x+1=31/32-2/2015
=(1/2+1/4+1/8+1/16+1/32)+(1+1+1+1+1)-6+x-1/x+1=31/32-2/2015
=31/32+5-6+x-1/x+1=31/32-2/2015
=5-6+x-1/x+1=31/32-2/2015-31/32
=-1+x-1/x+1=-2/2015
=x-1/x+1=-2/2015- -1
=x-1/x+1=2013/2015
=>x=2014

a)\(\left(\frac{1}{2}-\frac{1}{3}\right).6^x+6^{x+2}=6^{15}+6^{18}\)
\(\frac{1}{6}.6^x+6^{x+2}=6^{15}\left(1+6^3\right)\)
\(\frac{1}{6}.6^x\left(1+6^3\right)=6^{15}.217\)
\(6^{x-1}.217=6^{15}.217\)
\(6^{x-1}=6^{15}\)
\(x-1=15\)
\(x=16\)
b) \(\left(\frac{1}{2}-\frac{1}{6}\right).3^{x+4}-4.3^x=3^{16}-4.3^{13}\)
\(\frac{1}{3}.3^x.4\left(3^4-1\right)=3^{13}.4\left(3^3-1\right)\)
\(3^x.4.\left(3^3-1\right)=3^{13}.4.\left(3^3-1\right)\)
\(3^x=3^{13}\)
\(x=13\)
\(\left(\frac{1}{2}-\frac{1}{6}\right).\left(3^x.3^4\right)-4.3^x=3^{16}-4.3^{13}\)
=> \(\frac{1}{3}.3^x.3^4-4.3^x=3^{16}-4.3^{13}\)
=> \(3^x.3^4-4.3^x=\left(3^{16}-4.3^{13}\right):\frac{1}{3}\)
=> \(3^x.3^4-4.3^x=-386339074,3\)
=> \(3^x.\left(3^4-4\right)=-386339074,3\)
=> \(3^x.77=-386339074,3\)
=> \(3^x=-386339074,3:77\)
=> \(3^x=-5017390,575\)
=> x = ... chắc tự ngồi tính đc

bạn giải câu hỏi của CHÓcho minh minh giải cho bạn câu này mình biết
giải cách cấu tạo số nghe

a)
200 - ( 2 . x + 6 ) = 8 . 2
200 - ( 2 . x + 6 ) = 16
2 . x + 6 = 200 - 16
2 . x + 6 = 184
x + 6 = 184 : 2
x + 6 = 92
x = 92 - 6
x = 86
b)
2 . x : 4 = 16
x : 4 = 16 : 2
x : 4 = 8
x = 8 . 4
x = 32
c)
2008 . x : 2008 . 5 = 2008 . 3
2008. ( x : 5 ) = 6024
x : 5 = 6024 : 2008
x : 5 = 3
x = 3 . 5
x = 15