Bài1: tìm x biết
a) l x - 3,5 l = 7,5
b) l x + \(\dfrac{4}{5}\) l - \(\dfrac{1}{2}\) = 0
c) 3,6 - l x - 0,4 l = 0
d) \(\dfrac{-5}{12}\) : | \(\dfrac{-5}{6}\) : x | = \(\dfrac{-5}{9}\)
e) | x - 3,5|+|4,5- x|=0
bài 2:tính hợp lý
a) (-4,3)=[(-7,5)=(4,3)]
b) 45,3 + [(7,3)+(-22)]
c) [(-11.7)+5.5]+[11.7+(2.5)]
d) [(-6.8)+(-56.9)]+[2.8+5.9]
1)
a) \(|x-3,5|=7,5\)
\(\Rightarrow x-3,5=7,5\)
hay \(x-3,5=-7,5\)
TH1 : \(x-3,5=7,5\Rightarrow x=7,5+3,5=11\)
TH2 : \(x-3,5=-7,5\Rightarrow x=-7,5+3,5=-4\)
b) \(|x+\dfrac{4}{5}|-\dfrac{1}{2}=0\)
\(\Rightarrow\left(x+\dfrac{4}{5}\right)-\dfrac{1}{2}=0\) (chỉ có 1 TH vì số 0 ko phải dương or âm)
\(\left(x+\dfrac{4}{5}\right)=0+\dfrac{1}{2}=\dfrac{1}{2}\)
\(x=\dfrac{1}{2}-\dfrac{4}{5}=\dfrac{5-8}{10}=\dfrac{-3}{10}\)
c) \(3,6-|x-0,4|=0\)
\(\Rightarrow3,6-\left(x-0,4\right)=0\) ( giải thích giống câu b )
\(\Rightarrow-\left(x-0,4\right)=0-3,6\)
\(\Rightarrow-\left(x-0,4\right)=-3,6\)
\(\Rightarrow-x+0,4=-3,6\) ( Phá dấu )
\(\Rightarrow-x=-3,6-0,4=-3,6+\left(-0,4\right)=-4\)
\(\Rightarrow x=4\)
d) \(-\dfrac{5}{12}:|\dfrac{-5}{6}:x|=\dfrac{-5}{9}\)
\(\Rightarrow-\dfrac{5}{12}:|\dfrac{-5}{6}:x|=\dfrac{-5}{9}\)
hay \(\Rightarrow-\dfrac{5}{12}:|\dfrac{-5}{6}:x|=\dfrac{5}{9}\)
TH1 : \(-\dfrac{5}{12}:\left(-\dfrac{5}{6}:x\right)=\dfrac{-5}{9}\Rightarrow\left(-\dfrac{5}{6}:x\right)=-\dfrac{5}{12}:\left(-\dfrac{5}{9}\right)\)
\(\Rightarrow\left(-\dfrac{5}{6}:x\right)=\dfrac{5}{12}.\dfrac{9}{5}=\dfrac{9}{12}=\dfrac{3}{4}\)
\(\Rightarrow x=-\dfrac{5}{6}:\dfrac{3}{4}=-\dfrac{5.4}{6.3}=-\dfrac{5.2}{3.3}=-\dfrac{10}{9}\)
TH2 : \(\Rightarrow-\dfrac{5}{12}:\left(-\dfrac{5}{6}:x\right)=\dfrac{5}{9}\)
\(\Rightarrow\)\(\left(-\dfrac{5}{6}:x\right)=-\dfrac{5}{12}:\dfrac{5}{9}=-\dfrac{5.9}{12.5}=-\dfrac{9}{12}=-\dfrac{3}{4}\)
\(\Rightarrow x=-\dfrac{5}{6}:\left(-\dfrac{3}{4}\right)=\dfrac{5}{6}.\dfrac{4}{3}=\dfrac{10}{9}\)
Vậy x = ....
e)
Vì \(|x-3,5|\ge0;|4,5-x|\ge0\) với mọi x
Do đó : \(|x-3,5|+|4,5-x|=0\)
\(\Rightarrow|x-3,5|=0;|4,5-x|=0\)
\(\Rightarrow x-3,5=0\) và \(4,5-x=0\)
\(\Rightarrow x=0+3,5=3,5\) và \(-x=0+4,5=4,5\Rightarrow x=-4,5\)
( không đồng thời xảy ra)
\(\Rightarrow\) Không tồn tại x thuộc Q để \(|x-3,5|+|4,5-x|=0\)
2)
a) Đề sai
b) (45,3 + 7,3) + (-22)
= 52,6 + (-22) = 30,6
c) [(-11.7) + (11.7)] + [5.5+10]
= 0 + 15.5 = 15.5
( Câu c bạn cho rối quá )
d) [(-6.8) + 2.8] + [(-56.9) + 5.9 ]
= (-4) + (-51) = 55
