Đáp án:
`a, | 3x + 4 |= 2|2 x - 9|`
Do `|3x+4| >= 0`
`|2x-9| >= 0 -> 2|2x-9| >= 0`
`=> 3x+4 = 2(2x-9)`
`-> 3x+4 = 4x - 18`
`-> 3x - 4x = -4-18`
`-> -7x = -22`
`-> x = 22/7`
Vậy `x=22/7`
`b, 8x-|4x + 1|=x +2`
`-> |4x+1| = 8x - (x+2)`
`-> |4x+1| = 7x - 2`
`->` $\left[\begin{matrix} 4x+1=7x-2\\ 4x+1=2-7x\end{matrix}\right.$
`->` $\left[\begin{matrix} 4x-7x=-1-2\\ 4x+7x=2-1\end{matrix}\right.$
`->` $\left[\begin{matrix} 3x=3\\11x=1\end{matrix}\right.$
`->` $\left[\begin{matrix} x=1\\x=1/11\end{matrix}\right.$
`c, |17x-5|-|17x+5|=0`
`=> |17x-5|=|17x+5|`
`=>` $\left[\begin{matrix} 17x-5=17x+5\\17x-5=-17x-5\end{matrix}\right.$
`=>` $\left[\begin{matrix} 17x-17x=5+5\\17x+17x=-5+5\end{matrix}\right.$
`=>` $\left[\begin{matrix} 0=10 ( L )\\34x=0\end{matrix}\right.$
`=> x = 0`
Vậy `x=0`
`d, |x-1|=2x-5`
`=>` $\left[\begin{matrix} x-1=2x-5\\x-1=-2x+5\end{matrix}\right.$
`=>` $\left[\begin{matrix} x-2x=1-5\\x+2x=1+5\end{matrix}\right.$
`=>` $\left[\begin{matrix} -x=-4\\3x=6\end{matrix}\right.$
`=>` $\left[\begin{matrix} x=4\\x=2\end{matrix}\right.$
Vậy `x in {4,2}`
