\(-\frac47-x:\frac13=-1\frac{1}{14}\)
K
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23 tháng 7 2018
a) \(x+2x+3x+...+100x=-213\)
\(\Rightarrow x.\left(1+2+3+...+100\right)=-213\)
\(\Rightarrow x.5050=-213\Rightarrow x=\frac{-213}{5050}\)
b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}-4\frac{1}{6}\)
\(\Rightarrow\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}-\frac{25}{6}\)
\(\Rightarrow\frac{1}{2}x-\frac{1}{3}=\frac{-47}{12}\)
\(\Rightarrow\frac{1}{2}x=\frac{-43}{12}\Rightarrow x=\frac{-43}{6}\)
d) \(\frac{x+1}{3}=\frac{x-2}{4}\Rightarrow4\left(x+1\right)=3\left(x-2\right)\Rightarrow4x+4=3x-6\)
\(\Rightarrow4x-3x=-6-4\Rightarrow x=-10\)
c) \(3\left(x-2\right)+2\left(x-1\right)=10\)
\(\Rightarrow3x-6+2x-2=10\)
\(\Rightarrow5x=18\Rightarrow x=\frac{18}{5}\)
23 tháng 7 2018
a) \(x+2x+3x+4x+...+100x=-213\)
\(x.\left(1+2+3+4+...+100\right)=-213\)
\(x.5050=-213\)
\(x=-\frac{213}{5050}\)
b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}-4\frac{1}{6}\)
\(\frac{1}{2}x-\frac{1}{3}=-\frac{47}{12}\)
\(\frac{1}{2}x=-\frac{43}{12}\)
\(x=\frac{-43}{6}\)
29 tháng 6 2018
a) \(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)
\(\Leftrightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}\)
\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
Vì \(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne=\)
Nên x + 1 = 0 => x = -1
b) \(\frac{x+1}{14}+\frac{x+2}{13}=\frac{x+3}{12}+\frac{x+4}{11}\)
\(\Leftrightarrow\frac{x+1}{14}+1+\frac{x+2}{13}+1=\frac{x+3}{12}+1+\frac{x+4}{11}+1\)
\(\Leftrightarrow\frac{x+15}{14}+\frac{x+15}{13}=\frac{x+15}{12}+\frac{x+15}{11}\)
\(\Leftrightarrow\frac{x+15}{14}+\frac{x+15}{13}-\frac{x+15}{12}-\frac{x+15}{11}=0\)
\(\Leftrightarrow\left(x+15\right)\left(\frac{1}{14}+\frac{1}{13}-\frac{1}{12}-\frac{1}{11}\right)=0\)
Vì \(\frac{1}{14}+\frac{1}{13}-\frac{1}{12}-\frac{1}{11}\ne0\)
Nên x +15 = 0 => x = -15
29 tháng 6 2018
a,\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)
\(\Rightarrow\left(x+1\right).\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\right)=\left(x+1\right).\left(\frac{1}{13}+\frac{1}{14}\right)\)
\(\Rightarrow\left(x+1\right).\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\right)-\left(x+1\right).\left(\frac{1}{13}+\frac{1}{14}\right)=0\)
\(\Rightarrow\left(x+1\right).\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
Vì \(\frac{1}{10}>\frac{1}{13};\frac{1}{11}>\frac{1}{14}\Rightarrow\frac{1}{10}+\frac{1}{11}>\frac{1}{13}+\frac{1}{14}\Rightarrow\frac{1}{10}+\frac{1}{11}+\frac{1}{12}>\frac{1}{13}+\frac{1}{14}\)
\(\Rightarrow\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}>0\)
\(\Rightarrow x+1=0\Rightarrow x=-1\)
b, Bạn cộng thêm 1 vào \(\frac{x+1}{14};\frac{x+1}{13};\frac{x+1}{12};\frac{x+1}{11}\)Mội bên phân số 1 đơn vị rồi áp dụng như bài 1
23 tháng 3 2020
\(1\frac{1}{7}-\frac{5}{7}< \frac{x}{7}< 2\frac{1}{14}-1\frac{3}{14}\)
=> \(\frac{8}{7}-\frac{5}{7}< \frac{x}{7}< \frac{29}{14}-\frac{17}{14}\)
=> \(\frac{3}{7}< \frac{x}{7}< \frac{12}{14}\)
=> \(\frac{3}{7}< \frac{x}{7}< \frac{6}{7}\)
=> 3 < x < 6
=> x thuộc { 3 ; 4 ; 5 ; 6 }
KN
16 tháng 2 2020
Từ hệ phương trình suy ra: \(4.14+\frac{14}{y}=1\)
\(\Rightarrow\frac{14}{y}=-55\Rightarrow y=\frac{-14}{55}\)
Thay y vào phương trình \(\frac{1}{x}+\frac{1}{y}=14\)giải được \(x=\frac{14}{251}\)
Vậy hệ có 1 nghiệm \(\left(\frac{14}{251};\frac{-14}{55}\right)\)
UI
16 tháng 2 2020
dk \(x,y\ne0\)
thay \(\frac{1}{x}+\frac{1}{y}=14\) vao pt 2 ta duoc
\(4.14+\frac{14}{y}=1\Leftrightarrow56+\frac{14}{y}=1\Leftrightarrow y=\frac{-14}{55}\)
thay \(y=\frac{-14}{55}\)
vao pt 1 \(\Rightarrow\frac{1}{x}-\frac{55}{14}=14\Leftrightarrow x=\frac{14}{251}\)tmdk
thu lai ta thay thoa man
vay \(\left\{x;y\right\}=\left\{\frac{14}{251};\frac{-14}{55}\right\}\)
28 tháng 3 2018
Thiếu một điều kiện \(x\) là số tự nhiên nữa nhé
Ta có :
\(1\frac{1}{7}-\frac{5}{7}< \frac{x}{7}< 2\frac{1}{14}-1\frac{3}{14}\)
\(\Leftrightarrow\)\(\frac{8}{7}-\frac{5}{7}< \frac{x}{7}< \frac{29}{14}-\frac{17}{14}\)
\(\Leftrightarrow\)\(\frac{3}{7}< \frac{x}{7}< \frac{12}{14}\)
\(\Leftrightarrow\)\(\frac{3}{7}< \frac{x}{7}< \frac{6}{7}\)
\(\Leftrightarrow\)\(3< x< 6\)
\(\Rightarrow\)\(x\in\left\{4;5\right\}\)
Vậy \(x\in\left\{4;5\right\}\)
Chúc bạn học tốt ~
\(-\frac47-x:\frac13=-1\frac{1}{14}\)
\(x:\frac13=-\frac47-\left(-\frac{15}{14}\right)\)
\(x:\frac13=-\frac{8}{14}-\left(-\frac{15}{14}\right)\)
\(x:\frac13=\frac{7}{14}\)
\(x=\frac{7}{14}\cdot\frac13\)
\(x=\frac{7}{42}\)
\(x=\frac16.\)
+ Vậy \(x=\frac16\).
\(\frac{-4}{7}-x:\frac13=-1\frac{1}{14}\)
\(\frac{-4}{7}-x:\frac13=\frac{-15}{14}\)
\(x:\frac13=\frac{-4}{7}-\frac{-15}{14}\)
\(x:\frac13=\frac{-4}{7}+\frac{15}{14}\)
x : \(\frac13\) = \(\frac{-8}{14}+\frac{15}{14}\)
x : \(\frac13=\frac12\)
x = \(\frac12\) . \(\frac13\)
x = \(\frac16\)
Vậy x = \(\frac16\)