Question

Giải pt

a)\(\left|x-2\right|=3\)

b)\(\left|x+1\right|=\left|2x+3\right|\)

c)\(\left|3x\right|=x+6\)

Answer 1

a/ |x-2| = 3

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

b/ |x+1| = |2x + 3|

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

c/ |3x|=x+6

\(\Leftrightarrow\left\{{}\begin{matrix}3x=x+6\\3x=-x-6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\x=-\dfrac{3}{2}\end{matrix}\right.\)

Answer 2

a)|x-2|=3

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

b)|x+1|=|2x-3|

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

c)|3x|=x+6

=>\(\left\{{}\begin{matrix}3x=x+6\\3x=-x-6\end{matrix}\right.\)=>\(\left\{{}\begin{matrix}x=3\\x=\frac{-3}{2}\end{matrix}\right.\)

chúc bạn học tốt!