Question

[ZephyZ]

 

d,|2x-1|=|x-2|

e,(x-2/3)+1=2x-5/4

f,|2x-1|-2=3

h,(2x+1)^3 = -1/7

i,|2x-1/3|-2/5=0

Answer 1

[Dang Tung]

h) Mình sửa đề vế phải là -1/27 nhé 

\(\left(2x+1\right)^3=-\dfrac{1}{27}=\left(-\dfrac{1}{3}\right)^3\\ \Rightarrow2x+1=-\dfrac{1}{3}\\ \Rightarrow2x=-\dfrac{1}{3}-1=-\dfrac{4}{3}\\ \Rightarrow x=-\dfrac{4}{3}:2=-\dfrac{2}{3}\)

i) \(\left|2x-\dfrac{1}{3}\right|-\dfrac{2}{5}=0\Rightarrow\left|2x-\dfrac{1}{3}\right|=\dfrac{2}{5}\\ \Rightarrow\left[{}\begin{matrix}2x-\dfrac{1}{3}=\dfrac{2}{5}\\2x-\dfrac{1}{3}=-\dfrac{2}{5}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=\dfrac{11}{15}\\2x=-\dfrac{1}{15}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{11}{30}\\x=-\dfrac{1}{30}\end{matrix}\right.\)

Answer 2

[Dang Tung]

d) \(\left|2x-1\right|=\left|x-2\right|\Rightarrow\left[{}\begin{matrix}2x-1=x-2\\2x-1=-\left(x-2\right)\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x-x=1-2\\2x-1=-x+2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\2x+x=1+2\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-1\\3x=3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x=1\end{matrix}\right.\)

e) \(\left(x-\dfrac{2}{3}\right)+1=2x-\dfrac{5}{4}\Rightarrow x-\dfrac{2}{3}+1=2x-\dfrac{5}{4}\\ \Rightarrow2x-x=\dfrac{5}{4}-\dfrac{2}{3}+1\\ \Rightarrow x=\dfrac{19}{12}\)

f) \(\left|2x-1\right|-2=3\Rightarrow\left|2x-1\right|=5\\ \Rightarrow\left[{}\begin{matrix}2x-1=5\\2x-1=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=6\\2x=-4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)