Tìm x biết :\(x+\frac{3x}{4}=\frac{7}{2}\)
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16 tháng 8 2019
1a) \(\left|\frac{3}{2}x+\frac{1}{2}\right|=\left|4x-1\right|\)
=> \(\orbr{\begin{cases}\frac{3}{2}x+\frac{1}{2}=4x-1\\\frac{3}{2}x+\frac{1}{2}=1-4x\end{cases}}\)
=> \(\orbr{\begin{cases}-\frac{5}{2}x=-\frac{3}{2}\\\frac{11}{2}x=\frac{1}{2}\end{cases}}\)
=> \(\orbr{\begin{cases}x=\frac{5}{3}\\x=\frac{1}{11}\end{cases}}\)
b) \(\left|\frac{5}{4}x-\frac{7}{2}\right|-\left|\frac{5}{8}x+\frac{3}{5}\right|=0\)
=>\(\left|\frac{5}{4}x-\frac{7}{2}\right|=\left|\frac{5}{8}x+\frac{3}{5}\right|\)
=> \(\orbr{\begin{cases}\frac{5}{4}x-\frac{7}{2}=\frac{5}{8}x+\frac{3}{5}\\\frac{5}{4}x-\frac{7}{2}=-\frac{5}{8}x-\frac{3}{5}\end{cases}}\)
=> \(\orbr{\begin{cases}\frac{5}{8}x=\frac{41}{10}\\\frac{15}{8}x=\frac{29}{10}\end{cases}}\)
=> \(\orbr{\begin{cases}x=\frac{164}{25}\\x=\frac{116}{75}\end{cases}}\)
c) TT
16 tháng 8 2019
a, \(\left|\frac{3}{2}x+\frac{1}{2}\right|=\left|4x-1\right|\)
=> \(\orbr{\begin{cases}\frac{3}{2}x+\frac{1}{2}=4x-1\\-\frac{3}{2}x-\frac{1}{2}=4x-1\end{cases}}\)
=> \(\orbr{\begin{cases}\frac{3}{2}x+\frac{1}{2}-4x=-1\\-\frac{3}{2}x-\frac{1}{2}-4x=-1\end{cases}}\)
=> \(\orbr{\begin{cases}x=\frac{3}{5}\\x=\frac{1}{11}\end{cases}}\)
\(b,\left|\frac{5}{4}x-\frac{7}{2}\right|-\left|\frac{5}{8}x+\frac{3}{5}\right|=0\)
=> \(\left|\frac{5}{4}x-\frac{7}{2}\right|-0=\left|\frac{5}{8}x+\frac{3}{5}\right|\)
=> \(\frac{\left|5x-14\right|}{4}=\frac{\left|25x+24\right|}{40}\)
=> \(\frac{10(\left|5x-14\right|)}{40}=\frac{\left|25x+24\right|}{40}\)
=> \(\left|50x-140\right|=\left|25x+24\right|\)
=> \(\orbr{\begin{cases}50x-140=25x+24\\-50x+140=25x+24\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{164}{25}\\x=\frac{116}{75}\end{cases}}\)
c, \(\left|\frac{7}{5}x+\frac{2}{3}\right|=\left|\frac{4}{3}x-\frac{1}{4}\right|\)
=> \(\orbr{\begin{cases}\frac{7}{5}x+\frac{2}{3}=\frac{4}{3}x-\frac{1}{4}\\-\frac{7}{5}x-\frac{2}{3}=\frac{4}{3}x-\frac{1}{4}\end{cases}}\)
=> \(\orbr{\begin{cases}x=-\frac{55}{4}\\x=-\frac{25}{164}\end{cases}}\)
Bài 2 : a. |2x - 5| = x + 1
TH1 : 2x - 5 = x + 1
=> 2x - 5 - x = 1
=> 2x - x - 5 = 1
=> 2x - x = 6
=> x = 6
TH2 : -2x + 5 = x + 1
=> -2x + 5 - x = 1
=> -2x - x + 5 = 1
=> -3x = -4
=> x = 4/3
Ba bài còn lại tương tự
24 tháng 1 2019
\(\frac{3}{x-5}=-\frac{4}{x+2}\)
\(\Leftrightarrow3\left(x+2\right)=\left(-4\right)\left(x-5\right)\)
\(\Leftrightarrow3x+6=-4x+20\)
\(\Leftrightarrow7x=14\)
\(\Leftrightarrow x=2\)
\(\frac{4}{x+2}=\frac{7}{3x+1}\)
\(\Leftrightarrow4\left(3x+1\right)=\left(x+2\right)7\)
\(\Leftrightarrow12+4=7x+14\)
\(\Leftrightarrow5x=10\)
\(\Leftrightarrow x=2\)
\(-\frac{3}{x+1}=\frac{4}{2-2x}\)
\(\Leftrightarrow\left(-3\right)\left(2-2x\right)=\left(x+1\right)4\)
\(\Leftrightarrow-6+6x=4x+4\)
\(\Leftrightarrow2x=10\)
\(\Leftrightarrow x=5\)
TT
1
22 tháng 6 2015
\(\frac{7}{8}\cdot\left(\frac{4}{7}-1\frac{1}{7}x\right)=0,75-3x\)
\(\Rightarrow\frac{1}{2}-x=0,75-3x\)
\(\Rightarrow-4x=0,75-\frac{1}{2}\)
\(\Rightarrow-4x=0,25\)
\(\Rightarrow x=0,25:\left(-4\right)=-0,0625\)
17 tháng 8 2017
Tìm số tự nhiên x: \(2^{x-1}+5.2^{x-2}=224\Leftrightarrow2.2^{x-2}+5.2^{x-2}=224\)
\(\Leftrightarrow2^{x-2}.\left(5+2\right)=224\Leftrightarrow2^{x-2}.7=224\)
\(\Rightarrow2^{x-2}=32\Leftrightarrow2^{x-2}=2^5\)\(\Rightarrow x-2=5\Leftrightarrow x=7\)
Vậy x=7
Tìm x biết: \(\frac{3}{7}=\frac{2x+1}{3x+5}\)
\(\Rightarrow3\left(3x+5\right)=7\left(2x+1\right)\Leftrightarrow9x+15=14x+7\)
\(\Leftrightarrow14x+7-\left(9x+15\right)=0\Rightarrow5x+\left(-8\right)=0\)
\(\Leftrightarrow5x=8\Rightarrow x=\frac{8}{5}\)
Vậy x=8/5
PP
1
6 tháng 11 2018
\(\frac{2x+1}{5}=\frac{3y-2}{7}=\frac{z+4}{9}=\frac{2x+3y-1}{6x}\)(1)
Áp dụng tính chất dãy tỉ sổ bằng nhau, ta được
\(\frac{2x+1}{5}=\frac{3y-2}{7}=\frac{z+4}{9}=\frac{2x+3y-1}{6x}=\frac{\left(2x+1\right)+\left(3y-2\right)}{5+7}=\frac{2x+3y-1}{12}\)
\(\Rightarrow\frac{2x+3y-1}{6x}=\frac{2x+3y-1}{12}\)
\(\Rightarrow\frac{12}{6x}=\frac{2x+3y-1}{2x+3y-1}=1\)
\(\Rightarrow\frac{2}{x}=1\)
\(\Rightarrow x=2\)
Thay x=2 vào (1), ta được
\(\frac{3y-2}{7}=\frac{z+4}{9}=\frac{2\cdot2+1}{5}=1\)
\(\Rightarrow\hept{\begin{cases}3y-2=7\\z+4=9\end{cases}}\Rightarrow\hept{\begin{cases}3y=9\\z=5\end{cases}}\Rightarrow\hept{\begin{cases}y=3\\z=5\end{cases}}\)
Vậy...hok tốt
Y
20 tháng 7 2019
a. \(\frac{-3}{2}-2x+\frac{3}{4}=-22\)2
=> \(-2x=-22+\frac{3}{2}-\frac{3}{4}\)
=> \(-2x=\frac{-85}{4}\)
=> \(x=\frac{-85}{4}:\left(-2\right)\)
=> \(x=\frac{85}{8}\)
b. \(\left(\frac{-2}{3}x-\frac{3}{5}\right).\left(\frac{3}{-2}-\frac{10}{3}\right)=\frac{2}{5}\)
=> \(\left(\frac{-2}{3}x-\frac{3}{5}\right).\frac{-29}{6}=\frac{2}{5}\)
=> \(\frac{-2}{3}x-\frac{3}{5}=\frac{2}{5}:\left(\frac{-29}{6}\right)\)
=> \(\frac{-2}{3}x-\frac{3}{5}=\frac{-12}{145}\)
=> \(\frac{-2}{3}x=\frac{-12}{145}+\frac{3}{5}\)
=> \(\frac{-2}{3}x=\frac{15}{29}\)
=> x = \(\frac{15}{29}:\frac{-2}{3}\)
=> x = \(\frac{-45}{58}\)
11 tháng 8 2016
1, ta co \(\frac{x}{5}=\frac{y}{6}=\frac{x}{20}=\frac{y}{24}\)
\(\frac{y}{8}=\frac{z}{7}=\frac{y}{24}=\frac{z}{21}\)
=>\(\frac{x}{20}=\frac{y}{24}=\frac{z}{21}=\frac{x+y-z}{20+24-21}=\frac{69}{23}=3\)
=>\(x=3\cdot20=60\)
\(y=3\cdot24=72\)
\(z=3\cdot21=63\)
11 tháng 8 2016
3. ta co \(\frac{x}{15}=\frac{y}{7}=\frac{z}{3}=\frac{t}{1}=\frac{x+y-z+t}{15-7+3-1}=\frac{10}{10}=1\)
=> \(x=1\cdot15=15\)
\(y=1\cdot7=7\)
\(z=1\cdot3=3\)
\(t=1\cdot1=1\)
27 tháng 8 2017
a) \(\frac{2}{3x}-\frac{3}{12}=\frac{4}{5}-\left(\frac{7}{x}-2\right)\)
\(\frac{2}{3x}+\left(\frac{7}{x}-2\right)=\frac{4}{5}+\frac{3}{12}\)
\(\frac{2}{3x}+\frac{7}{x}-2=\frac{21}{20}\)
\(\frac{2}{3x}+\frac{7}{x}=\frac{61}{20}\)
\(\frac{2}{3x}+\frac{21}{3x}=\frac{61}{20}\)
\(\frac{23}{3x}=\frac{61}{20}\)
\(3x=\frac{460}{61}\)
\(x=\frac{460}{183}\)
b) \(\left(\frac{3}{2}-\frac{2}{-5}\right):x-\frac{1}{2}=\frac{3}{2}\)
\(\frac{19}{10}:x-\frac{1}{2}=\frac{3}{2}\)
\(\frac{19}{10}:x=2\)
\(x=\frac{19}{20}\)
NT
0
\(x+\frac{3x}{4}=\frac{7}{2}\)
\(x+3x.\frac{1}{4}=\frac{7}{2}\)
\(x.\left(1+3.\frac{1}{4}\right)=\frac{7}{2}\)
\(x.\left(1+\frac{3}{4}\right)=\frac{7}{2}\)
\(x.\frac{7}{4}=\frac{7}{2}\)
\(x=\frac{7}{2}:\frac{7}{4}\)
\(x=2\)
\(x+\frac{3x}{4}=\frac{7}{2}\)
\(\Rightarrow\frac{4x+3x}{4}=\frac{7}{2}\)
\(\Rightarrow\frac{7x}{4}=\frac{14}{4}\)
\(\Rightarrow7x=14\)
\(\Rightarrow x=14:7\)
\(\Rightarrow x=2\)
Vậy x = 2
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