Question

giải các phương trình chứa dấu giá trị tuyệt đối sau:

a) // x - 4 / + 8 / = 9

b) // x + 5 / + 9 / = 10

Answer 1

a)//x-4/+8/=9

\(\Leftrightarrow\left[{}\begin{matrix}\left|x-4\right|+8=9\\\left|x-4\right|+8=-9\left(loai\right)\end{matrix}\right.\)

\(\Leftrightarrow\left|x-4\right|=1\)

\(\Leftrightarrow\left[{}\begin{matrix}x-4=1\\x-4=-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=3\end{matrix}\right.\)

b)TT\(\Rightarrow\left|x+5\right|+9=10\)

\(\Leftrightarrow\left|x+5\right|=1\)

\(\Leftrightarrow\left[{}\begin{matrix}x+5=1\\x+5=-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-6\end{matrix}\right.\)

Answer 2

a)

\(\left||x-4|+8\right|=9\)

\(\Leftrightarrow\left|x-4\right|=1\)

\(\Leftrightarrow\left[{}\begin{matrix}x-4=1\\x-4=-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=3\end{matrix}\right.\)

b)

\(\left||x+5|+9\right|=10\)

\(\Leftrightarrow\left|x+5\right|+9=10\)

\(\Leftrightarrow\left|x+5\right|=1\)

\(\Leftrightarrow\left[{}\begin{matrix}x+5=1\\x+5=-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-6\end{matrix}\right.\)