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3:
a: (a-b+c)-(c-b-a)
=a-b+c-c+b+a
=2a
b: \(-\left(a-b\right)+\left(b-c+a\right)-\left(a+b-c\right)\)
\(=-a+b+b-c+a-a-b+c\)
\(=b-a\)
c: \(-\left(a-b-c\right)-\left(-a+b+c\right)-\left(a-b+c\right)\)
\(=-a+b+c+a-b-c-a+b-c\)
\(=-a+b-c\)
2:
a: \(12-\left(-12\right)=12+12=24\)
b: \(-\left(35-49\right)+\left(27-49\right)=-35+49+27-49\)
=-35+27
=-8
c: \(47-\left(59-63\right)+\left(63-47\right)\)
\(=47-59+63+63-47\)
=126-59
=67
d: \(-\left(-20\right)-\left(-30\right)-70\)
=20+30-70
=50-70
=-20
a) \(x+546=46\\ x=46-546\\ x=-500\)
b) \(2x-19\times3=27\\ 2x-57=27\\ 2x=27+57\\ 2x=84\\ x=84:2\\ x=42\)
c) \(x+12=23+3\times3^4\\ x+12=23+3\times81\\ x=23+243-12\\ x=254\)
d) \(x-12=3-3\times2^4\\ x-12=3-3\times16\\ x=3-48+12\\ x=-33\)
e) \(\left(27-x\right)\left(x+9\right)=0\\ \Rightarrow\left[{}\begin{matrix}27-x=0\\x+9=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=27\\x=-9\end{matrix}\right.\)
f) \(\left(-x\right)\left(x-43\right)=0\\ \Rightarrow\left[{}\begin{matrix}-x=0\\x-43=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=43\end{matrix}\right.\)
Lời giải:
a. $=-(37+63)+[25+(-25)]+(-9)=-100+0+(-9)=-(100+9)=-109$
b. $=[1+(-3)]+[5+(-7)]+....+[21+(-23)]$
$=\underbrace{(-2)+(-2)+....+(-2)}_{6}=(-2).6=-12$
c. $=-(280+20)+[-(79+21)]=-300+(-100)=-(300+100)=-400$
d. $=[-(27+43)]+[-(208+102)]=-70+(-310)=-(70+310)=-380$
e. $=(38+120)-(12+46)=158-58=100$
f. $=9+15+11+24=(9+11)+(15+24)=20+39=59$
Câu 3:
a) \(\dfrac{12}{36}=\dfrac{12:12}{36:12}=\dfrac{1}{3}\)
\(\dfrac{-16}{20}=\dfrac{-16:4}{20:4}=\dfrac{-4}{5}\)
b) \(\dfrac{21}{105}=\dfrac{21:21}{105:21}=\dfrac{1}{5}\)
\(\dfrac{35}{150}=\dfrac{35:5}{150:5}=\dfrac{7}{30}\)
Câu 4:
a) \(\dfrac{3}{10}+\dfrac{5}{10}=\dfrac{3+5}{10}=\dfrac{8}{10}=\dfrac{4}{5}\)
b) Ta có: \(\left(-27\right)\cdot36+64\cdot\left(-27\right)+23\cdot\left(-100\right)\)
\(=\left(-27\right)\cdot\left(64+36\right)+23\cdot\left(-100\right)\)
\(=-27\cdot100-23\cdot100\)
\(=100\left(-27-23\right)\)
\(=-50\cdot100=-5000\)
c) \(\dfrac{5}{8}+\dfrac{3}{12}=\dfrac{15}{24}+\dfrac{6}{24}=\dfrac{21}{24}=\dfrac{7}{8}\)
d) Ta có: \(\dfrac{-2}{17}+\dfrac{3}{19}+\dfrac{-15}{17}+\dfrac{16}{19}+\dfrac{5}{6}\)
\(=\left(-\dfrac{2}{17}+\dfrac{-15}{17}\right)+\left(\dfrac{3}{19}+\dfrac{16}{19}\right)+\dfrac{5}{6}\)
\(=-1+1+\dfrac{5}{6}\)
\(=\dfrac{5}{6}\)
Bài 2:
a: =>x-35=-23
=>x=12
b: =>|x-8|=13
=>x-8=13 hoặc x-8=-13
=>x=21 hoặc x=-5
Bài 1:
a: =42-98-42+12-12=-98
b: =10x4x3x(-25)=40x(-25)x3=-1000x3=-3000
a) ( 2993 + 215 ) - 1993
= ( 2993 - 1993 ) + 215
= 1000 + 215
= 1215.
b) 2043 - ( 1560 + 43 )
= 2043 - 43 + 1560
= 2000 + 1560
= 3560
c) 46 - ( 12 - 20 )
= 46 - 12 - 20
= 34 - 20
= 14
d) 27 + ( 19 - 36 )
= 27 + 19 - 36
= 46 - 36
= 10
đúng nha!