Tìm x thuộc Z a) |x – 7|= 6 b) 2|x – 3|= 24 c) – 3|x + 2|=( – 12) d) |x + 1|= – (- 10)

0 bình luận về “Tìm x thuộc Z a) |x – 7|= 6 b) 2|x – 3|= 24 c) – 3|x + 2|=( – 12) d) |x + 1|= – (- 10)”

1. $a)$ `|x – 7|= 6`

   `=> x-7=6` hoặc `x-7=-6`

   $+)$ `x-7=6`

   `x=6+7`

   `x=13`

   $+)$ `x-7=-6`

   `x=-6+7`

   `x=1`

   Vậy `x\in {1; 13}.`

   $b)$ `2|x – 3|= 24`

   `=> |x-3|=24: 2`

   `=> |x-3|=12`

   `=> x-3=12` hoặc `x-3=-12`

   $+)$ `x-3=12`

   `x=12+3`

   `x=15`

   $+)$ `x-3=-12`

   `x=-12+3`

   `x=-9`

   Vậy `x\in {-9; 15}.`

   $c)$ `- 3|x + 2|=( – 12)`

   `=> |x+2|=(-12): (-3)`

   `=> |x+2|=4`

   `=> x+2=4` hoặc `x+2=-4`

   $+)$ `x+2=4`

   `x=4-2`

   `x=2`

   $+)$ `x+2=-4`

   `x=-4-2`

   `x=-4+(-2)`

   `x=-6`

   Vậy `x\in {-6; 2}.`

   $d)$ `|x + 1|= – (- 10)`

   `=> |x+1|=10`

   `=> x+1=10` hoặc `x+1=-10`

   $+)$ `x+1=10`

   `x=10-1`

   `x=9`

   $+)$ `x+1=-10`

   `x=-10-1`

   `x=-10+(-1)`

   `x=-11`

   Vậy `x\in {-11; 9}.`

    

   Bình luận

2. Giải thích các bước giải:

   `a) |x – 7|= 6`
   `=>`\(\left[ \begin{array}{l}x-7=6\\x-7=-6\end{array} \right.\) 
   `=>`\(\left[ \begin{array}{l}x=6+7\\x=-6+7\end{array} \right.\) 
   `=>`\(\left[ \begin{array}{l}x=13\\x=1\end{array} \right.\) 
   `b) 2|x – 3|= 24`
   `=>|x-3|=24:2`
   `=>|x-3|=12`
   `=>`\(\left[ \begin{array}{l}x-3=12\\x-3=-12\end{array} \right.\) 
   `=>`\(\left[ \begin{array}{l}x=12+3\\x=-12+3\end{array} \right.\) 
   `=>`\(\left[ \begin{array}{l}x=15\\x=-9\end{array} \right.\) 
   `c) – 3|x + 2|=( – 12)`
   `=>|x+2|=(-12):(-3)`
   `=>|x+2|=4`
   `=>`\(\left[ \begin{array}{l}x+2=4\\x+2=-4\end{array} \right.\) 
   `=>`\(\left[ \begin{array}{l}x=4-2\\x=-4-2\end{array} \right.\)
   `=>`\(\left[ \begin{array}{l}x=2\\x=-6\end{array} \right.\) 
   `d) |x + 1|= – (- 10)`
   `=>|x+1|=10`
   `=>`\(\left[ \begin{array}{l}x+1=10\\x+1=-10\end{array} \right.\) 
   `=>`\(\left[ \begin{array}{l}x=10-1\\x=-10-1\end{array} \right.\)
   `=>`\(\left[ \begin{array}{l}x=9\\x=-11\end{array} \right.\) 

   Bình luận