Question

Giải các phương trình chứa dấu giá trị tuyệt đối :

a) |x+3| = 3x+1

b) |x+4| = 2x-5

c) |x-4+3| = 5

d) |-5x| - 16 = 3x

e)

|-3x| = x-8

Help me

Answer 1

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

\(\Leftrightarrow\left\{{}\begin{matrix}x>=-\dfrac{1}{3}\\\left(4x+4\right)\left(2x-2\right)=0\end{matrix}\right.\Leftrightarrow x=1\)

b: \(\Leftrightarrow\left\{{}\begin{matrix}x>=\dfrac{5}{2}\\\left(2x-5-x-4\right)\left(2x-5+x+4\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>=\dfrac{5}{2}\\\left(x-9\right)\left(3x-1\right)=0\end{matrix}\right.\Leftrightarrow x=9\)

c: =>|x-1|=5

=>x-1=5 hoặc x-1=-5

=>x=6 hoặc x=-4