Tìm x biết
a)\(\left|2x-3\right|-x=\)\(\left|2-x\right|\)
b)\(\left|x+3\right|+\left|x+1\right|=\)\(3x\)
c)\(2005=\left|x-4\right|+\left|x-10\right|+\left|x+101\right|+\left|x+990\right|+\left|x+1000\right|\)
d)\(\left|x+\frac{1}{2}\right|+\left|x+\frac{1}{6}\right|+\left|x+\frac{1}{20}\right|+..+\left|x+\frac{1}{110}\right|=11x\)
A=1.2.3+2.3.4+3.4.5+...+98.99.1004A=1.2.3.4+2.3.4.4+3.4.5.4+...+98.99.100.44A=1.2.3.(4-0)+2.3.4.(5-1)+...+98.99.100.(101-97)4A=1.2.3.4+2.3.4.5-1.2.3.4+...+98.99.100.101-97.98.99.1004A=1.2.3.4-1.2.3.4+2.3.4.5-...-97.98.99.100+98.99.100.1014A=98.99.100.1014A=97990200A=979902004A=24497550
a, Vào câu hỏi tương tự nhé
b, Vì \(\hept{\begin{cases}\left|x+3\right|\ge0\\\left|x+1\right|\ge0\end{cases}\Rightarrow\left|x+3\right|+\left|x+1\right|\ge0\Rightarrow3x\ge0\Rightarrow x\ge0}\)
=> x+3+x+1=3x
=> 2x+4=3x
=>x=4
c, \(\left|x-4\right|+\left|x-10\right|+\left|x+101\right|+\left|x+990\right|+\left|x+1000\right|=\left|4-x\right|+\left|10-x\right|+\left|x+101\right|+\left|x+990\right|+\left|x+1000\right|\)
Có \(\left|4-x\right|\ge4-x;\left|10-x\right|\ge10-x;\left|x+990\right|\ge x+990;\left|x+1000\right|\ge x+1000\)
=>\(\left|4-x\right|+\left|10-x\right|+\left|x+101\right|+\left|x+990\right|+\left|x+1000\right|\)
=> \(2005\ge4-x+10-x+x+990+x+1000+\left|x+101\right|\)
=> \(2005\ge\left|x+101\right|+2004\)
=> \(\left|x+101\right|\le1\)
=> \(x+101\in\left\{-1;0;1\right\}\Rightarrow x\in\left\{-102;-101;-100\right\}\)
d, tương tự b