Question

Tìm x biết:

a) |2x+3|=x+2

b) |3-x|=1-3x

c) |x-\(\frac{1}{5}\)|=\(\frac{1}{5}\)-x

d) (x-5)^x+1=(x-5)^x+11

e) 2010-|x-2010|=0

f) |3x-4|+|3x+5|=-9

Answer 1

a: |2x+3|=x+2

\(\Leftrightarrow\left\{{}\begin{matrix}x>=-2\\\left(2x+3+x+2\right)\left(2x+3-x-2\right)=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=-2\\\left(3x+5\right)\left(x+1\right)=0\end{matrix}\right.\)

hay x=-1

d: \(\left(x-5\right)^{x+11}=\left(x-5\right)^{x+1}\)

\(\Leftrightarrow\left(x-5\right)\left(x-4\right)\left(x-6\right)=0\)

hay \(x\in\left\{5;4;6\right\}\)

e: =>|x-2010|=2010

=>x-2010=2010 hoặc x-2010=-2010

=>x=4020 hoặc x=0