Bài 1.
`a)` `|2x|=x-6`
$⇔\left\{\begin{matrix}x-6\ge 0\\\left[\begin{array}{l}2x=x-6\\2x=6-x\end{array}\right.\end{matrix}\right.$$⇔\left\{\begin{matrix}x\ge 6\\\left[\begin{array}{l}x=-6\ (KTM)\\3x=6\end{array}\right.\end{matrix}\right.$$⇔\begin{cases}x\ge 6\\x=2\ (TM)\end{cases}$
Vậy nghiệm của pt là $x=2$
$\\$
`b)` `|-3x|=x-8`
$⇔\left\{\begin{matrix}x-8\ge 0\\\left[\begin{array}{l}-3x=x-8\\-3x=8-x\end{array}\right.\end{matrix}\right.$$⇔\left\{\begin{matrix}x\ge 8\\\left[\begin{array}{l}-4x=-8\\-2x=8\end{array}\right.\end{matrix}\right.$$⇔\left\{\begin{matrix}x\ge 8\\\left[\begin{array}{l}x=2\ (KTM)\\x=-4\ (KTM)\end{array}\right.\end{matrix}\right.$
Vậy pt vô nghiệm
$\\$
`c)` `|4x|=2x+12`
`<=>|2x|=x+6`
$⇔\left\{\begin{matrix}x+6\ge 0\\\left[\begin{array}{l}2x=x+6\\2x=-x-6\end{array}\right.\end{matrix}\right.$$⇔\left\{\begin{matrix}x\ge -6\\\left[\begin{array}{l}x=6\\3x=-6\end{array}\right.\end{matrix}\right.$$⇔\left\{\begin{matrix}x\ge -6\\\left[\begin{array}{l}x=6\ (TM)\\x=-2\ (TM)\end{array}\right.\end{matrix}\right.$
Vậy pt có nghiệm $x=6;x=-2$
$\\$
`d)` `|-5x|-16=3x`
`<=>|5x|=3x+16`
$⇔\left\{\begin{matrix}3x+16\ge 0\\\left[\begin{array}{l}5x=3x+16\\5x=-3x-16\end{array}\right.\end{matrix}\right.$$⇔\left\{\begin{matrix}x\ge \dfrac{-16}{3}\\\left[\begin{array}{l}2x=16\\8x=-16\end{array}\right.\end{matrix}\right.$$⇔\left\{\begin{matrix}x\ge \dfrac{-16}{3}\\\left[\begin{array}{l}x=8\ (TM)\\x=-2\ (TM)\end{array}\right.\end{matrix}\right.$
Vậy pt có nghiệm là: $x=8;x=-2$
Bài 2.
`a)` `||x-1|+2|=7` $(1)$
Ta có: `|x-1|\ge 0` với mọi $x$
`=>|x-1|+2\ge 2>0` với mọi $x$
`(1)<=>|x-1|+2=7`
`<=>|x-1|=5`
$⇔\left[\begin{array}{l}x-1=5\\x-1=-5\end{array}\right.$$⇔\left[\begin{array}{l}x=6\\x=-4\end{array}\right.$
Vậy pt có nghiệm là: $x=6;x=-4$
$\\$
`b)` `|2-x|-|2x-3|=0`
`<=>|2-x|=|2x-3|`
$⇔\left[\begin{array}{l}2-x=2x-3\\2-x=3-2x\end{array}\right.$$⇔\left[\begin{array}{l}-3x=-5\\x=1\end{array}\right.$
$⇔\left[\begin{array}{l}x=\dfrac{5}{3}\\x=1\end{array}\right.$
Vậy pt có nghiệm là: `x=5/ 3;x=1`
