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\(\frac{1}{4}+\frac{1}{3}:3.x=-5\)
\(\frac{1}{9}.x=-5-\frac{1}{4}\)
\(\frac{1}{9}.x=-\frac{21}{4}\)
\(x=-\frac{21}{4}:\frac{1}{9}\)
\(x=-\frac{189}{4}\)
\(\frac{1}{4}+\frac{1}{3}:3.x=-5\)
\(\frac{1}{4}+\frac{1}{9}x=-5\)
\(\frac{1}{9}x=-5-\frac{1}{4}\)
\(\frac{1}{9}x=\frac{-20}{4}-\frac{1}{4}\)
\(\frac{1}{9}x=\frac{-21}{4}\)
\(x=\frac{-21}{4}:\frac{1}{9}\)
\(x=\frac{-21}{4}.9\)
\(x=\frac{-189}{4}\)
Bài 1:
\(\frac{3}{5}+\frac{4}{15}=\frac{9}{15}+\frac{4}{15}=\frac{13}{15}\)
\(\frac{5}{6}:\frac{-7}{12}=\frac{5}{6}.\frac{-12}{7}=\frac{-60}{42}=\frac{-10}{7}\)
\(\frac{-21}{24}:\frac{-14}{8}=\frac{-21}{24}.\frac{-8}{14}=\frac{168}{336}=\frac{1}{2}\)
\(\frac{4}{5}:\frac{-8}{15}=\frac{4}{5}.\frac{-15}{8}=\frac{-60}{40}=\frac{-3}{2}\)
\(\frac{5}{12}-\frac{-7}{6}=\frac{5}{12}+\frac{7}{6}=\frac{5}{12}+\frac{14}{12}=\frac{19}{12}\)
\(\frac{-15}{16}.\frac{8}{25}=\frac{-120}{400}=\frac{-3}{10}\)
Bài 2 :
\(6\frac{4}{5}-\left(1\frac{2}{3}+3\frac{4}{5}\right)\)
\(=\frac{34}{5}-\left(\frac{5}{3}+\frac{19}{5}\right)\)
\(=\frac{34}{5}-\frac{5}{3}-\frac{19}{5}\)
\(=\left(\frac{34}{5}-\frac{19}{5}\right)-\frac{5}{3}\)
\(=3-\frac{5}{3}\)
\(=\frac{4}{3}\)
\(6\frac{5}{7}-\left(1\frac{2}{3}+2\frac{5}{7}\right)\)
\(=\frac{47}{7}-\left(\frac{5}{3}+\frac{19}{7}\right)\)
\(=\frac{47}{7}-\frac{5}{3}-\frac{19}{7}\)
\(=\left(\frac{47}{7}-\frac{19}{7}\right)-\frac{5}{3}\)
\(=4-\frac{5}{3}\)
\(=\frac{7}{3}\)
\(\frac{4}{19}.\frac{-3}{7}+\frac{-3}{7}.\frac{15}{19}+\frac{5}{7}\)
\(=\left(\frac{4}{19}+\frac{15}{19}\right).\frac{-3}{7}+\frac{5}{7}\)
\(=1.\frac{-3}{7}+\frac{5}{7}\)
\(=\frac{-3}{7}+\frac{5}{7}\)
\(=\frac{2}{7}\)
\(\frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}\)
\(=\frac{5}{9}.\left(\frac{7}{13}+\frac{9}{13}-\frac{3}{13}\right)\)
\(=\frac{5}{9}.1\)
\(=\frac{5}{9}\)
Câu hỏi 1 : 29 Câu hỏi 2 : {-1;3} Câu hỏi 3 : -60 Câu hỏi 4: {-19;-15} Câu hỏi 5: đề sai
Câu hỏi 6: 99 Câu hỏi 7: 981 Câu hỏi 8: 36 Câu hỏi 9 sai đề Câu hỏi 10 sai đề
Ta có 3x + 3x + 1 + 3x + 2 = 1053
=> 3x(1 + 31 + 32) = 1053
=> 3x(1 + 3 + 9) = 1053
=> 3x . 13 = 1053
=> 3x = 1053 : 13 = 81
=> x = 4
3 x + 3 x+1 + 3 x+2 = 1053
3x+3x.31+3x.32=1053
3x(1+31+32)=1053
3x.(1+3+9)=1053
3x.13=1053
3x=1053:13
3x=81
3x=34
=>x=4
a) Ta có:
\(\frac{9}{x}=\frac{y}{5}\Rightarrow xy=45\)
Mà \(45=5.9=9.5=\left(-5\right)\left(-9\right)=\left(-9\right)\left(-5\right)\)
Vậy x=1;y=2 hoặc x=2;y=1 hoặc x=-1;y=-2 hoặc x=-2;y=-1
b) Ta có: \(\frac{n+1}{n-1}=\frac{\left(n-1\right)+2}{n-1}=1+\frac{2}{n-1}\left(n\ne1\right)\)
Để A nguyên \(\Leftrightarrow\frac{2}{n-1}\) nguyên
\(\Leftrightarrow n-1\inƯ\left(2\right)=\left\{-1;-2;0;1;2\right\}\)
\(\Rightarrow n\in\left\{-1;0;2;3\right\}\)
c) Gọi abcd là số cần tìm
Ta có: a: 6 cách
b: 5 cách
c: 4 cách
d: 3 cách
==> có> 6.5.4.3=360 số có 4 chữ số khác nhau được lập nên từ các chữ số đã cho
Ta có: \(\left(x^2-3\right).\left(x^2-36\right)\le0\)
\(\Rightarrow\)\(\orbr{\begin{cases}x^2-3\ge0\\x^2-36\le0\end{cases}\Leftrightarrow\orbr{\begin{cases}x^2\ge3\\x^2\le36\end{cases}\Leftrightarrow}\orbr{\begin{cases}x\ge\sqrt{3}ho\text{ặc}x\le-\sqrt{3}\\x\le6ho\text{ặc}x\ge-6\end{cases}}}\)
\(\orbr{\begin{cases}x^2-3\le0\\x^2-36\ge0\end{cases}\Leftrightarrow\orbr{\begin{cases}x^2\le3\\x^2\ge36\end{cases}\Leftrightarrow}\orbr{\begin{cases}x\le\sqrt{3}ho\text{ặc}x\ge-\sqrt{3}\\x\ge6ho\text{ặc}x\le-6\end{cases}}}\)
KL:................................................................................................................
( x^2 - 3 )( x^2 - 36 ) \(\le0\)
TH1 : ( x^2 - 3 )( x^2 - 36 ) = 0
=> x^2 - 3 = 0 hoac x^2 - 36 = 0
=> x^2 = 3 hoac x^2 = 36
=> x = \(\sqrt{3}\)hoac bang 6 , -6
TH2 : ( x^2 - 3 )( x^2 - 36 ) < 0
=> x^2 - 3 am va x^2 - 36 duong hoac x^2 - 36 am va x^2 - 3 duong
TH x^2 - 3 am ( 1 ) va x^2 - 36 duong ( 2 )
Xet ( 1 ) thi :
=> x^2 < 2
=> x thuoc 1,0,-1
Nhung de x^2 - 36 duong ( 2 ) thi IxI > 6
Ma 1,0,-1 deu < 6
=> x \(\varnothing\)
TH x^2 - 36 am ( 1 ) va x^2 - 3 duong ( 2 )
Xet ( 1 ) thi :
I x I < 6
=> x \(\in\left\{5,4,3,2,1,0,-1,-2,-3,-4,-5\right\}\)
Xet ( 2 ) thi :
I x I > 2
=> x thuoc { 5,4,3,-3,-4,-5 }
Vay x \(\in\left\{\sqrt{3},6,5,4,3,-3,-4,-5,-6\right\}\)
3 ( x - 1 ) + \(\frac{1}{2}=\frac{-7}{4}\)
3 ( x - 1 ) = \(\frac{-7}{4}-\frac{1}{2}\)
3 ( x - 1 ) = \(\frac{-9}{4}\)
x - 1 = \(\frac{-9}{4}\div3\)
x - 1 = \(\frac{-3}{4}\)
x = \(\frac{-3}{4}+1\)
x = \(\frac{1}{4}\)
3(x - 1) + \(\frac{1}{2}\) = \(\frac{-7}{4}\)
3(x - 1) = \(\frac{-7}{4}\) - \(\frac{1}{2}\)
3(x - 1) = \(\frac{-9}{4}\)
x - 1 = \(\frac{-9}{4}\) : 3
x - 1 = \(\frac{-3}{4}\)
x = \(\frac{-3}{4}\) + 1
x = \(\frac{1}{4}\)