1,a,\(\left|x+2\right|=x+3\Leftrightarrow\orbr{\begin{cases}x+2=x+3\\x+2=-x-3\end{cases}}\)

                                      \(\Leftrightarrow\orbr{\begin{cases}x-x=3-2\\x+x=-3-2\end{cases}\Leftrightarrow\orbr{\begin{cases}0=1\left(voly\right)\\x=\frac{-5}{2}\end{cases}}}\)

b, \(|x-2|=2-x\Leftrightarrow\orbr{\begin{cases}x-2=2-x\\x-2=x-2\end{cases}}\)

                                    \(\Leftrightarrow\orbr{\begin{cases}x+x=2+2\\x-x=-2+2\end{cases}\Rightarrow x=2}\)

c,\(\left|2x-1\right|=3\Leftrightarrow\orbr{\begin{cases}2x-1=3\\2x-1=-3\end{cases}}\)

                             \(\Leftrightarrow\orbr{\begin{cases}2x=4\\2x=-2\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2\\x=-1\end{cases}}}\)

d,\(\left|x-12\right|=x\Leftrightarrow\orbr{\begin{cases}x-12=x\\x-12=-x\end{cases}\Leftrightarrow\orbr{\begin{cases}0=12\left(voly\right)\\x=6\end{cases}}}\)

A=1+(2-3-3+5)+(6-7-8+9)+....+(98-99-100+101)+102

=1+0+0+....+102=103

b) |1-2x|>7

=> 1-2x>7 hoặc 1-2x<-7

=> 2x<-6 hoặc 2x>8

=> x<-3 hoặc x>4

a) => \(\left(\frac{1}{3}-\frac{5}{6}x\right)^3=\frac{5}{6}-\frac{21}{54}=\frac{24}{54}=\frac{4}{9}\)

=> \(\frac{1}{3}-\frac{5}{6}x=\sqrt[3]{\frac{4}{9}}\) => \(\frac{5}{6}x=\frac{1}{3}-\sqrt[3]{\frac{4}{9}}\) => \(x=\frac{6}{5}.\left(\frac{1}{3}-\sqrt[3]{\frac{4}{9}}\right)\)

b) \(\frac{1}{3}\left(\frac{1}{2}x-1\right)^4=\frac{1}{12}-\frac{1}{16}=\frac{1}{48}\) => \(\left(\frac{1}{2}x-1\right)^4=\frac{3}{48}=\frac{1}{16}\)

=> \(\frac{1}{2}x-1=\frac{1}{2}\) hoặc  \(\frac{1}{2}x-1=-\frac{1}{2}\)

=> \(\frac{1}{2}x=\frac{3}{2}\) hoặc \(\frac{1}{2}x=\frac{1}{2}\) => x = 3 hoặc x = 1

c) \(\left(1+5\right).\left(\frac{3}{5}\right)^{x-1}=\frac{54}{25}\) => \(\left(\frac{3}{5}\right)^{x-1}=\frac{9}{25}=\left(\frac{3}{5}\right)^2\)

=> x - 1= 2 => x = 3

d) \(\left(1+\left(\frac{2}{3}\right)^2\right).\left(\frac{2}{3}\right)^x=\frac{101}{243}\) => \(\frac{13}{9}.\left(\frac{2}{3}\right)^x=\frac{101}{243}\)

=> \(\left(\frac{2}{3}\right)^x=\frac{101}{243}:\frac{13}{9}=\frac{101}{351}\) (có lẽ đề sai)

2) \(\frac{1}{27^{11}}=\frac{1}{\left(3^3\right)^{11}}=\frac{1}{3^{33}}\); \(\frac{1}{81^8}=\frac{1}{\left(3^4\right)^8}=\frac{1}{3^{32}}\)

Vì 3³³ > 3³² => \(\frac{1}{3^{33}}\) < \(\frac{1}{3^{32}}\) => \(\frac{1}{27^{11}}\) < \(\frac{1}{81^8}\)

b) \(\frac{1}{3^{99}}=\frac{1}{\left(3^3\right)^{33}}=\frac{1}{27^{33}}

nhjeu wa bạn giải 1 mjk luôn đi

https://olm.vn/hoi-dap/detail/23609978644.html

\(|x-7|+13=25\)

\(|x-7|=12\)

\(\Rightarrow\orbr{\begin{cases}x-7=12\\x-7=-12\end{cases}\Leftrightarrow\orbr{\begin{cases}x=19\\x=-5\end{cases}}}\)

\(|x-3|-16=-4\\ \Rightarrow|x-3|=14\)

\(\Rightarrow\orbr{\begin{cases}x-3=14\\x-3=-14\end{cases}\Leftrightarrow\orbr{\begin{cases}x=17\\x=-11\end{cases}}}\)

\(26-Ix+9I=-13\)

\(\Rightarrow|x+9|=39\)

\(\Rightarrow\orbr{\begin{cases}x+9=39\\x+9=-39\end{cases}\Leftrightarrow\orbr{\begin{cases}x=30\\x=-48\end{cases}}}\)

\(|x-5|=3\)

\(\Rightarrow\orbr{\begin{cases}x-5=3\\x-5=-3\end{cases}\Leftrightarrow\orbr{\begin{cases}x=8\\x=2\end{cases}}}\)

\(|1-x|=7\)

\(\Rightarrow\orbr{\begin{cases}1-x=7\\1-x=-7\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-6\\x=8\end{cases}}}\)

\(|2x+5|=1\)

\(\Rightarrow\orbr{\begin{cases}2x+5=1\\2x+5=-1\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=-3\end{cases}}}\)

\(\text{11 _ 12 +13 _ 14 + 15 - 16 + 17 _ 18 + 19 _20}\)

\(=\left(11-12\right)+\left(13-14\right)+\left(15-16\right)+\left(17-18\right)+\left(19-20\right)\)

\(=-1+\left(-1\right)+\left(-1\right)+\left(-1\right)+\left(-1\right)\)

\(=-5\)

\(\text{101 _ 102 _ ( - 103 ) _ 104 _ ( - 105 ) _ 106 _ ( -107 ) _ 108 _ ( - 109 ) _ 110}\)

\(=\left(101-102\right)+\left(-\left(-103\right)-104\right)+\left(-\left(-105\right)-106\right)\)\(+\left(-\left(-107\right)-108\right)+\left(-\left(-109\right)-110\right)\)

\(=-1+\left(-1\right)+\left(-1\right)+\left(-1\right)+\left(-1\right)\)

\(=-5\)

\(\text{1 + ( - 3 ) +5 + ( -7 ) + ... + ( - 1999 ) + 2001}\)

\(=\left(1+\left(-3\right)\right)+\left(5+\left(-7\right)\right)+...+\left(\left(-1999\right)+2001\right)\)

\(=-2+\left(-2\right)+...+\left(-2\right)\)Có 500 thừa số (-2)

\(=\left(-2\right).500\)

\(=-1000\)

\(\text{1 + ( -2 ) + 3 + ( -4) + ... + 2001 + ( - 2002)}\)

\(=\left(1+\left(-2\right)\right)+\left(3+\left(-4\right)\right)+...+\left(2001+\left(-2002\right)\right)\)

\(=-1+\left(-1\right)+...+\left(-1\right)\)Có 1000 thừa số (-1)

\(=\left(-1\right).1000\)

\(=-1000\)

chúc bạn học tốt

a) 105*x-20-18-16-...-2=19+17+15+...+3+1

105*x=1+2+3+4+...+20

105*x=\(\frac{\left(20+1\right)x20}{2}\)

105*x=210

x=2

Vậy x = 2

b) 1-6+11-16+21-26+...+91-96+101

=101-96+91-86+...+21-16+11-6+1

=(101-96)+(91-86)+...+(21-16)+(11-6)+1

=5+5+...+5+5+1                ( có (101-6):5+1);2=10 số 5)

=5x10+1=51

a)105xX-20-18-16-...-2=19+17+15+...+3+1

105xX-(20+18+16+...+2)=19+17+15+...+3+1

105xX-110=100

105xX=100+110

105xX=210

X=210:105

X=2