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\(60\%x+0,4x+x:3=2\\ \Leftrightarrow\left(60\%+0,4+\dfrac{1}{3}\right)x=2\\ \Rightarrow\dfrac{4}{3}x=2\\ \Rightarrow x=\dfrac{3}{2}\)
\(60\%x+0,4x+x:3=2\)
\(x.\left(60\%+0,4+\dfrac{1}{3}\right)=2\)
\(x.\dfrac{4}{3}=2\)
\(x=2:\dfrac{4}{3}\)
\(x=\dfrac{3}{2}\)
Bài 1 :
\(A=\dfrac{n+1}{n+2}\) có giá trị nguyên âm, dương khi
\(n+1⋮n+2\)
\(\Rightarrow n+1-\left(n+2\right)⋮n+2\)
\(\Rightarrow n+1-n-2⋮n+2\)
\(\Rightarrow-1⋮n+2\)
\(\Rightarrow n+2\in\left\{-1;1\right\}\)
\(\Rightarrow n\in\left\{-3;-1\right\}\left(n\in Z\right)\)
Bài 2 :
\(1+\left(-\dfrac{1}{60}\right)+\dfrac{19}{120}< \dfrac{x}{36}+\left(-\dfrac{1}{60}\right)< \dfrac{58}{90}+\dfrac{59}{72}+\left(-\dfrac{1}{60}\right)\)
\(\Rightarrow1+\dfrac{19}{120}< \dfrac{x}{36}< \dfrac{58}{90}+\dfrac{59}{72}\)
\(\Rightarrow\dfrac{139}{120}< \dfrac{x}{36}< \dfrac{232}{360}+\dfrac{295}{360}\)
\(\Rightarrow\dfrac{417}{360}< \dfrac{10x}{360}< \dfrac{527}{360}\)
\(\Rightarrow417< 10x< 527\)
\(\Rightarrow10x\in\left\{420;430;440;450;460;470;480;490;500;510;520\right\}\)
\(\Rightarrow x\in\left\{42;43;44;45;46;47;48;49;50;51;52\right\}\)
34+25x=2960⇒25x=2960−34⇒25x=2960−3.1560⇒25x=29−4560⇒25x=−1660=−415⇒x=−415:25⇒x=−415.52⇒x=−23Vậyx=−23
Bài 1:
\(101\cdot125+101\cdot25-101\cdot50\)
\(=101\cdot\left(125+25-50\right)\)
\(=101\cdot100\)
\(=10100\)
Bài 2:
\(76\cdot115+56\cdot24+59\cdot24\)
\(=76\cdot115+24\cdot\left(56+59\right)\)
\(=76\cdot115+24\cdot115\)
\(=115\cdot\left(76+24\right)\)
\(=115\cdot100\)
\(=11500\)
a) \(\dfrac{6}{13}:\left(\dfrac{1}{2}-x\right)=\dfrac{15}{39}\)
\(\dfrac{1}{2}-x=\dfrac{6}{13}:\dfrac{15}{39}\)
\(\dfrac{1}{2}-x=\dfrac{6}{5}\)
\(x=\dfrac{1}{2}-\dfrac{6}{5}\)
\(x=-\dfrac{7}{10}\)
b) \(3\times\left(\dfrac{x}{4}+\dfrac{x}{28}+\dfrac{x}{70}+\dfrac{x}{130}\right)=\dfrac{60}{13}\)
\(3\times x\times\left(\dfrac{1}{4}+\dfrac{1}{28}+\dfrac{1}{70}+\dfrac{1}{130}\right)=\dfrac{60}{13}\)
\(x\times\left(\dfrac{3}{1\times4}+\dfrac{3}{4\times7}+\dfrac{3}{7\times10}+\dfrac{3}{7\times13}\right)=\dfrac{60}{13}\)
\(x\times\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}\right)=\dfrac{60}{13}\)
\(x\times\left(1-\dfrac{1}{13}\right)=\dfrac{60}{13}\)
\(x\times\dfrac{12}{13}=\dfrac{60}{13}\)
\(x=\dfrac{60}{13}:\dfrac{12}{13}\)
\(x=5\)
a)Vì 84⋮x➩ x∈ƯC(84;180)
180⋮x
Ta có:
24=23.3
180=22.32.5
ƯCLN(...)=22.3=12
ƯC(...)=Ư(12)={1;2;3;4;6;12}
Vì 84⋮x;180⋮x và x≥6
⇔x={6;12}
b)x⋮28;x⋮56;x⋮70➩x∈BC(...)
Ta có:28=22.7
56=23.7
70=2.5.7
BCNN(...)=23.5.7=280
BC(...)=B(280)={0;280;560;840;...}
Vì x⋮28;x⋮56;x⋮70 và 500<x<600
⇔x=280
c)x⋮12➩x=B(12)
B(12)={0;12;24;36;48;60;72;...}
Vì x⋮12 và x<60
⇔ x={0;12;24;48}
\(B=4x^2-y^2-1=\left(2x-y\right)\left(2x+y\right)-1\)
Thay x = 234 ; y = 456 vào B ta được :
\(=\left(468-456\right)\left(468+456\right)-1\)
\(=12.924-1=11087\)
