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\(\frac{7}{x+2}=\frac{3}{3x-2}\)
\(\Leftrightarrow7\cdot\left(3x-2\right)=3\cdot\left(x+2\right)\)
\(\Leftrightarrow21x-14=3x+6\)
\(\Leftrightarrow21x-3x=6+14\)
\(\Leftrightarrow18x=20\)
\(\Leftrightarrow x=\frac{10}{9}\)
Bài 1 : Ta có:
\(\frac{7+\frac{7}{11}+\frac{7}{23}+\frac{7}{31}}{9+\frac{9}{11}+\frac{9}{23}+\frac{9}{31}}\)
= \(\frac{7.\left(1+\frac{1}{11}+\frac{1}{23}+\frac{1}{31}\right)}{9.\left(1+\frac{1}{11}+\frac{1}{23}+\frac{1}{31}\right)}\)
= \(\frac{7}{9}\)
Bài 2 :
\(\frac{x}{2}+\frac{3x}{4}+\frac{5x}{6}=\frac{10}{24}\)
=> \(\frac{12x+18x+20x}{24}=\frac{10}{24}\)
=> 50x = 10
=> x = 10 : 50
=> x = 1/5
Bài 3 : Để A nhận giá trị nguyên thì 3 \(⋮\)x + 3
<=> x + 3 \(\in\)Ư(3) = {1; -1; 3; -3}
Lập bảng :
x + 3 | 1 | -1 | 3 | -3 |
x | -2 | -4 | 0 | -6 |
Vậy
\(x+\frac{3x}{4}=\frac{7}{2}\)
\(x+3x.\frac{1}{4}=\frac{7}{2}\)
\(x.\left(1+3.\frac{1}{4}\right)=\frac{7}{2}\)
\(x.\left(1+\frac{3}{4}\right)=\frac{7}{2}\)
\(x.\frac{7}{4}=\frac{7}{2}\)
\(x=\frac{7}{2}:\frac{7}{4}\)
\(x=2\)
\(x+\frac{3x}{4}=\frac{7}{2}\)
\(\Rightarrow\frac{4x+3x}{4}=\frac{7}{2}\)
\(\Rightarrow\frac{7x}{4}=\frac{14}{4}\)
\(\Rightarrow7x=14\)
\(\Rightarrow x=14:7\)
\(\Rightarrow x=2\)
Vậy x = 2
_Chúc bạn học tốt_
\(\left|x+\frac{7}{3}\right|=\left|x-\frac{7}{2}\right|\)
Vì \(x+\frac{7}{3}\ne x-\frac{7}{2}\)nên \(x+\frac{7}{3}=\frac{7}{2}-x\)
\(\Leftrightarrow x+x=\frac{7}{2}-\frac{7}{3}\)
\(\Leftrightarrow2x=\frac{21}{6}-\frac{14}{6}\)
\(\Leftrightarrow2x=\frac{7}{6}\)
\(\Leftrightarrow x=\frac{7}{6}\div2\)
\(\Leftrightarrow x=\frac{7}{12}\)
b) \(\left|2x-\frac{1}{3}\right|=\left|3x\left(-\frac{2}{3}\right)\right|\)
\(\Leftrightarrow\left|2x-\frac{1}{3}\right|=\left|-2x\right|\)
\(\Leftrightarrow\orbr{\begin{cases}2x-\frac{1}{3}=-2x\\2x-\frac{1}{3}=2x\end{cases}}\Leftrightarrow\orbr{\begin{cases}4x=\frac{1}{3}\\x\in\left\{\varnothing\right\}\end{cases}}\Leftrightarrow x=\frac{1}{12}\)
Vậy \(x=\frac{1}{12}\)
\(\frac{11}{4}:\frac{3}{2}:\left|4x-\frac{1}{3}\right|=\frac{7}{2}\)
\(\Leftrightarrow\frac{3}{2}:\left|4x-\frac{1}{3}\right|=\frac{11}{4}:\frac{7}{2}\)
\(\Leftrightarrow\frac{3}{2}:\left|4x-\frac{1}{3}\right|=\frac{11}{14}\)
\(\Leftrightarrow\left|4x-\frac{1}{3}\right|=\frac{3}{2}:\frac{11}{14}\)
\(\Leftrightarrow\left|4x-\frac{1}{3}\right|=\frac{21}{11}\)
\(\Leftrightarrow\orbr{\begin{cases}4x-\frac{1}{3}=\frac{21}{11}\\4x-\frac{1}{3}=-\frac{21}{11}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{37}{66}\\x=-\frac{13}{33}\end{cases}}\)
Bài dưới tương tự
0,5x-2/3x=7/12
=>(1/2-2/3).x=7/12
=>-1/6x=7/12
=>x=7/12:1/6
=>x=7/2
b, x:4 1/3=-2,5
=>x:13/3=-2,5
=>x=-5/2x13/3
=>x=-13
c,5,5x=13/15
=>11/2x=13/15
=>x=13/15:11/2
=>x=26/165
d,(3x/7+1):-4=-1/28
=>3x/7+1=-1/28x(-4)
=>3x/7+1=-1/7
=>3x/7=-1/7-1
=>3x/7=-8/7
=>3x=-8/7x7
=>3x=8
=>x=8:3
=>x=8/3
\(0,5x-\frac{2}{3}x=\frac{7}{12}\)
\(\frac{1}{2}x-\frac{2}{3}x=\frac{7}{12}\)
\(\left(\frac{1}{2}-\frac{2}{3}\right)x=\frac{7}{12}\)
\(\frac{-1}{6}x=\frac{7}{12}\)
\(x=-21\)
b,c,d tương tự
x=22/7;-20/7