3 tìm x biết
\(\dfrac{111}{37}< x< \dfrac{91}{13}x\)e Z
b) \(\dfrac{-84}{14}< x< \dfrac{108}{9}\)
4 Tìm x
a ) \(\dfrac{x-1}{9}=\dfrac{8}{3}\)
b) \(\dfrac{-x}{4}=\dfrac{-9}{x}\)
c ) \(\dfrac{x}{4}=\dfrac{18}{x+1}\)
Tìm x ϵ Z, biết:
a, \(\dfrac{111}{37}\)< x< \(\dfrac{91}{13}\)
b, \(\dfrac{-84}{14}< 3x< \dfrac{108}{9}\)
Cảm ơn nha!
a)
\(\dfrac{111}{37}=3< x< \dfrac{91}{13}=7\)
Vậy x = {4;5;6}
b)
\(-\dfrac{84}{14}=-6< 3x< \dfrac{108}{9}=12\Leftrightarrow-2< x< 4\)
Vậy x = {-1;0;1;2;3}
a, Ta có : \(\dfrac{111}{37}< x< \dfrac{91}{13}\)
\(\Rightarrow3< x< 7\)
Mà x là số nguyên .
\(\Rightarrow x\in\left\{4;5;6\right\}\)
b, Ta có : \(-\dfrac{84}{14.3}< x< \dfrac{108}{9.3}\)
\(\Rightarrow-2< x< 4\)
Mà x là số nguyên .
\(\Rightarrow x\in\left\{-1;0;1;2;3\right\}\)
Giải:
a) \(\dfrac{111}{37}< x< \dfrac{91}{13}\)
\(\Rightarrow3< x< 7\)
\(\Rightarrow x\in\left\{4;5;6\right\}\)
b) \(\dfrac{-84}{14}< 3x< \dfrac{108}{9}\)
\(\Rightarrow-6< 3x< 12\)
\(\Rightarrow3x\in\left\{-3;0;3;6;9\right\}\)
\(\Rightarrow x\in\left\{-1;0;1;2;3\right\}\)
Bài 1: Tìm x thuộc Z:
\(a,\dfrac{111}{37}< x< \dfrac{91}{13}\) \(b,\dfrac{-84}{14}< 3x< \dfrac{108}{9}\)
Bài 2: Cho A = \(\dfrac{3n-5}{n+4}\). Tìm n thuộc Z để A có giá trị nguyên.
bài 2:để Z là số nguyên thì 3n-5 \(⋮\)n+4
\(\Rightarrow[(3n-5)-3(n+4)]⋮(n+4)\)
\(\Rightarrow(3n-5-3n-12)⋮(n+4)\)
\(\Rightarrow-17⋮n+4\)
\(\Rightarrow n+4\inƯ(17)\)={1;-1;17;-17}
\(\Rightarrow\)n\(\in\){-3;-5;13;-21}
2. Để phân số \(A=\dfrac{3n-5}{n+4}\in Z\)
\(\Leftrightarrow\left\{{}\begin{matrix}3n-5⋮n+4\\3n+12⋮n+4\end{matrix}\right.\)
\(\Leftrightarrow17⋮n+4\)
Vì \(n\in Z\Leftrightarrow n+4\in Z;n+4\inƯ\left(17\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}n+4=1\\n+4=17\\n+4=-1\\n+4=-17\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=-3\\n=13\\n=-5\\n=-21\end{matrix}\right.\)
Vậy ....
a)\(\dfrac{7}{8}\)x\(\dfrac{3}{13}\)+\(\dfrac{4}{9}\)x\(\dfrac{4}{13}\)
b)\(\dfrac{6}{5}\)+\(\dfrac{7}{3}\)+\(\dfrac{8}{9}\)
c)23: \(\dfrac{5}{14}\)+\(\dfrac{6}{7}\)+\(\dfrac{4}{9}\)
d)\(4\dfrac{1}{4}\)+\(7\dfrac{3}{7}\)-\(2\dfrac{4}{17}\)
e)8-(9\(\dfrac{2}{11}\)+\(\dfrac{8}{33}\))
a, \(\dfrac{7}{8}\) \(\times\) \(\dfrac{3}{13}\) + \(\dfrac{4}{9}\) \(\times\) \(\dfrac{4}{13}\)
= \(\dfrac{1}{13}\) \(\times\)( \(\dfrac{21}{8}\) + \(\dfrac{16}{9}\))
= \(\dfrac{1}{13}\) \(\times\)( \(\dfrac{189}{72}\) + \(\dfrac{128}{72}\))
= \(\dfrac{1}{13}\) \(\times\) \(\dfrac{317}{73}\)
= \(\dfrac{317}{949}\)
b, \(\dfrac{6}{5}\) + \(\dfrac{7}{3}\) + \(\dfrac{8}{9}\)
= \(\dfrac{54}{45}\) + \(\dfrac{105}{45}\) + \(\dfrac{40}{45}\)
= \(\dfrac{199}{45}\)
c, 23 : \(\dfrac{5}{14}\) + \(\dfrac{6}{7}\) + \(\dfrac{4}{9}\)
= \(\dfrac{322}{5}\) + \(\dfrac{6}{7}\) + \(\dfrac{4}{9}\)
= \(\dfrac{20286}{315}\) + \(\dfrac{270}{315}\) + \(\dfrac{140}{315}\)
= \(\dfrac{20696}{315}\)
d, 4\(\dfrac{1}{4}\) + 7\(\dfrac{3}{7}\) - 2\(\dfrac{4}{17}\)
= 4 + \(\dfrac{1}{4}\) + 7 + \(\dfrac{3}{7}\) - 2 - \(\dfrac{4}{17}\)
= (4+7-2) + (\(\dfrac{1}{4}\) + \(\dfrac{3}{7}\) - \(\dfrac{4}{17}\))
= 9 + \(\dfrac{119}{476}\) + \(\dfrac{204}{476}\) - \(\dfrac{112}{476}\)
= 9\(\dfrac{211}{476}\) = \(\dfrac{4495}{476}\)
e, 8 - (9\(\dfrac{2}{11}\) + \(\dfrac{8}{33}\))
= 8 - 9 - \(\dfrac{2}{11}\) - \(\dfrac{8}{33}\)
= -1 - \(\dfrac{2}{11}\) - \(\dfrac{8}{33}\)
= \(\dfrac{-33}{33}\) - \(\dfrac{-6}{33}\) - \(\dfrac{8}{33}\)
= - \(\dfrac{47}{33}\)
Tìm x, biết:
a) \(\dfrac{2}{5}\) + \(\dfrac{3}{4}\): x = \(\dfrac{-1}{2}\)
b) \(\dfrac{5}{7}\) - \(\dfrac{2}{3}\) . x = \(\dfrac{4}{5}\)
c) \(\dfrac{1}{2}\) x + \(\dfrac{2}{3}\) x = \(\dfrac{-2}{3}\)
d) \(\dfrac{4}{7}\)x - x= \(\dfrac{-9}{14}\)
a, 2/5 + 3/4 : x = -1/2
3/4 : x = -1/2 - 2/5
3/4 : x = -9/10
x = 3/4 : -9/10
x = -5/6
b, 5/7 - 2/3 . x = 4/5
2/3 . x = 4/5 + 5/7
2/3 . x = 53/35
x = 53/35 : 2/3
x = 159/70
c và d mình làm dược nhưng ko ghi được cái suy ra
Tìm x, y, z, t ∈ Z biết:
a, \(\dfrac{5}{x}=\dfrac{-10}{12}\) b, \(\dfrac{4}{-6}=\dfrac{x+3}{9}\) c, \(\dfrac{x-1}{25}=\dfrac{4}{x-1}\) d, \(\dfrac{x+1}{y}=\dfrac{-3}{5}\)
e, \(\dfrac{-12}{6}=\dfrac{x}{5}=\dfrac{-y}{3}=\dfrac{Z}{-17}=\dfrac{-t}{-9}\)
h, \(\dfrac{-24}{-6}=\dfrac{x}{3}=\dfrac{4}{y^2}=\dfrac{Z^3}{-2}\)
a) \(\dfrac{5}{x}=\dfrac{-10}{12}.\Rightarrow x=-6.\)
b) \(\dfrac{4}{-6}=\dfrac{x+3}{9}.\Rightarrow x+3=-6.\Leftrightarrow x=-9.\)
c) \(\dfrac{x-1}{25}=\dfrac{4}{x-1}.\left(đk:x\ne1\right).\Leftrightarrow\dfrac{x-1}{25}-\dfrac{4}{x-1}=0.\)
\(\Leftrightarrow\dfrac{x^2-2x+1-100}{25\left(x-1\right)}=0.\Leftrightarrow x^2-2x-99=0.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=11.\\x=-9.\end{matrix}\right.\) \(\left(TM\right).\)
a)\(\dfrac{2}{3}\)x-1=\(\dfrac{3}{2}\)
b)| 5x - \(\dfrac{1}{2}\)| - \(\dfrac{2}{7}\)= 25%
c)\(\dfrac{x-3}{4}\)=\(\dfrac{16}{x-3}\)
d)\(\dfrac{-8}{13}\)+\(\dfrac{7}{17}+\dfrac{21}{31}\)<x≤\(\dfrac{-9}{14}\)+4+\(\dfrac{5}{-14}\)(xϵZ)
a) Ta có: \(\dfrac{2}{3}x-1=\dfrac{3}{2}\)
\(\Leftrightarrow x\cdot\dfrac{2}{3}=\dfrac{5}{2}\)
hay \(x=\dfrac{5}{2}:\dfrac{2}{3}=\dfrac{5}{2}\cdot\dfrac{3}{2}=\dfrac{15}{4}\)
b) Ta có: \(\left|5x-\dfrac{1}{2}\right|-\dfrac{2}{7}=25\%\)
\(\Leftrightarrow\left|5x-\dfrac{1}{2}\right|=\dfrac{1}{4}+\dfrac{2}{7}=\dfrac{15}{28}\)
\(\Leftrightarrow\left[{}\begin{matrix}5x-\dfrac{1}{2}=\dfrac{15}{28}\\5x-\dfrac{1}{2}=\dfrac{-15}{28}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}5x=\dfrac{29}{28}\\5x=\dfrac{-1}{28}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{29}{140}\\x=\dfrac{-1}{140}\end{matrix}\right.\)
c) Ta có: \(\dfrac{x-3}{4}=\dfrac{16}{x-3}\)
\(\Leftrightarrow\left(x-3\right)^2=64\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=8\\x-3=-8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=11\\x=-5\end{matrix}\right.\)
d) Ta có: \(\dfrac{-8}{13}+\dfrac{7}{17}+\dfrac{21}{31}\le x\le\dfrac{-9}{14}+4-\dfrac{5}{14}\)
\(\Leftrightarrow\dfrac{3246}{6851}\le x\le3\)
\(\Leftrightarrow x\in\left\{1;2;3\right\}\)
Cho \(A=\dfrac{2\sqrt{x}+4}{\sqrt{x}-3}\); \(B=\dfrac{\sqrt{x}}{3+\sqrt{x}}+\dfrac{x+9}{9-x}\) \(\left(x\ge0;x\ne9\right)\). Biết \(C=\dfrac{B}{A}\). Tìm \(x\in Z\) để \(C< \dfrac{-1}{3}\).
\(C=\left(\dfrac{x-3\sqrt{x}-x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\right)\cdot\dfrac{\sqrt{x}-3}{2\sqrt{x}+4}\)
\(=\dfrac{-3}{2\sqrt{x}+4}\)
Để \(C< -\dfrac{1}{3}\) thì \(\dfrac{-3}{2\sqrt{x}+4}+\dfrac{1}{3}< 0\)
\(\Leftrightarrow-9+2\sqrt{x}+4< 0\)
\(\Leftrightarrow\sqrt{x}< \dfrac{5}{2}\)
hay \(0\le x< \dfrac{25}{4}\)
Cho \(A=\dfrac{2\sqrt{x}+4}{\sqrt{x}-3}\) và \(B=\dfrac{\sqrt{x}}{3+\sqrt{x}}+\dfrac{x+9}{9-x}\) (\(x\ge0;x\ne9\))
a, Rút gọn B.
b, Biết \(C=\dfrac{B}{A}\). Tìm \(x\in Z\) để \(C< -\dfrac{1}{3}\).
a: \(B=\dfrac{\sqrt{x}}{\sqrt{x}+3}-\dfrac{x+9}{x-9}\)
\(=\dfrac{x-3\sqrt{x}-x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{-3}{\sqrt{x}-3}\)
tìm x , biết:
a) \(x\) : \(4\dfrac{1}{3}\) = -2,5 b) \(\dfrac{3}{5}x\) + \(\dfrac{1}{4}\) = \(\dfrac{1}{10}\)
c) \(2\dfrac{7}{9}\) \(-\) \(\dfrac{12}{13}x\) = \(\dfrac{7}{9}\) d)\(\dfrac{-2}{3}-\dfrac{1}{3}\)\(\left(2x-5\right)=\dfrac{3}{2}\)
a, \(x\) : \(\dfrac{13}{3}\) = -2,5
\(x\) = -2,5 . \(\dfrac{13}{3}\)
\(x\) = \(\dfrac{65}{6}\)
b,\(\dfrac{3}{5}\)\(x\) = \(\dfrac{1}{10}-\)\(\dfrac{1}{4}\)
\(\dfrac{3}{5}x\) = \(\dfrac{-3}{20}\)
\(x\) = \(\dfrac{-3}{20}\) : \(\dfrac{3}{5}\)
\(x\) = \(\dfrac{-1}{4}\)
c, \(\dfrac{25}{9}-\dfrac{12}{13}x=\dfrac{7}{9}\)
\(\dfrac{12}{13}x\)\(=\dfrac{25}{9}-\dfrac{7}{9}\)
\(\dfrac{12}{13}x=2\)
\(x=2:\dfrac{12}{13}\)
\(x=\dfrac{13}{6}\)