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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
C
24 tháng 9 2019
a) Đặt \(x-1=a\)
\(pt\Leftrightarrow\frac{13}{a}+\frac{5}{2a}=\frac{6}{3a}\)
\(\Leftrightarrow\frac{31}{2a}=\frac{6}{3a}\)
\(\Leftrightarrow\frac{31}{2}=2\)(vô lí)
Vậy pt vô nghiệm
24 tháng 9 2019
a) \(\frac{13}{x-1}+\frac{5}{2x-2}=\frac{6}{3x-3}\)
\(\frac{13}{x-1}+\frac{5}{2\left(x-1\right)}=\frac{6}{3\left(x-1\right)}\)
\(\frac{13}{x-1}+\frac{5}{2\left(x-1\right)}=\frac{2}{x-1}\)
\(\frac{31}{2\left(x-1\right)}=\frac{2}{x-1}\)
\(\frac{31}{2}=2\)
=> không có x thỏa mãn đề bài.
b) \(\frac{1}{x-1}+\frac{-2}{3}\left(\frac{3}{4}-\frac{6}{5}\right)=\frac{5}{2-2x}\)
\(\frac{1}{x-1}+\frac{-2}{3}.\frac{-9}{20}=\frac{5}{2\left(1-x\right)}\)
\(\frac{1}{x-1}-\frac{-18}{60}=\frac{5}{2\left(1-x\right)}\)
\(\frac{1}{x-1}+\frac{3}{10}=\frac{5}{2\left(1-x\right)}\)
\(10\left(1-x\right)+3\left(x-1\right)\left(1-x\right)=25\left(x-1\right)\)
\(7-4x-3x^2=25x-25\)
\(7-4x-3x^2-25x+25=0\)
\(32-29x-3x^2=0\)
\(3x^2+29x-30=0\)
\(3x^2+32x-3x-32=0\)
\(x\left(3x+32\right)-\left(3x+32\right)=0\)
\(\left(3x+32\right)\left(x-1\right)=0\)
\(\orbr{\begin{cases}3x+32=0\\x-1=0\end{cases}}\)
\(\orbr{\begin{cases}x=-\frac{32}{3}\\x=1\end{cases}}\)
BN
1
25 tháng 11 2016
Ta có:\(\frac{x+1}{4}=\frac{2x-3}{5}=\frac{3x-2}{9y}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x+1}{4}=\frac{2x-3}{5}=\frac{3x-2}{9y}=\frac{x+1+2x-3}{4+5}=\frac{3x-2}{9}\)
Vì \(\frac{3x-2}{9y}=\frac{3x-2}{9}\Rightarrow9y=9\Rightarrow y=1\)
\(\Rightarrow\frac{x+1}{4}=\frac{3x-2}{9}\)
\(\Rightarrow9x+9=12x-8\)
\(9x-12x=-8-9\)
\(-3x=-17\)
\(x=\frac{17}{3}\)
NT
3
14 tháng 11 2017
\(\frac{2x-1}{-3}=\frac{3x+2}{5}\)
\(\Leftrightarrow5\left(2x-1\right)=-3\left(3x+2\right)\)
\(\Leftrightarrow10x-5=-9x-6\)
\(\Leftrightarrow10x+9x=-6+5\)
\(\Leftrightarrow19x=-1\)
\(\Leftrightarrow x=-\frac{1}{19}\)
LV
1
9 tháng 2 2018
=> 7-x+5/2-2x-2/3 = 5
=> 53/6 - 3x = 5
=> 3x = 53/6 - 5 = 23/6
=> x = 23/6 : 3 = 23/18
Vậy x = 23/18
Tk mk nha
LA
0
30 tháng 1 2022
c: \(\Leftrightarrow\left[{}\begin{matrix}2x+\dfrac{4}{5}=x-\dfrac{3}{2}\\2x+\dfrac{4}{5}=\dfrac{3}{2}-x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{23}{10}\\x=\dfrac{7}{30}\end{matrix}\right.\)
b: \(\Leftrightarrow\left|3x-2\right|=9-4x\)
\(\Leftrightarrow\left\{{}\begin{matrix}x< =\dfrac{9}{4}\\\left(3x-2\right)^2-\left(4x-9\right)^2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< =\dfrac{9}{4}\\\left(3x-2-4x+9\right)\left(3x-4+4x-9\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x< =\dfrac{9}{4}\\\left(7-x\right)\left(7x-13\right)=0\end{matrix}\right.\Leftrightarrow x=\dfrac{13}{7}\)
11 tháng 3 2019
a.\(\frac{1}{2}-\left(x-\frac{1}{3}\right)=\frac{1}{6}\)
\(x-\frac{1}{3}=\frac{1}{2}-\frac{1}{6}\)
\(x-\frac{1}{3}=\frac{1}{3}\)
\(x=\frac{2}{3}\)
11 tháng 3 2019
\(a.\frac{1}{2}-\left(x-\frac{1}{3}\right)=\frac{1}{6}\)
\(\Leftrightarrow\frac{1}{2}-x+\frac{1}{3}=\frac{1}{6}\)
\(\Leftrightarrow\frac{5}{6}-x=\frac{1}{6}\)
\(\Leftrightarrow\frac{5}{6}-\frac{1}{6}=x\)
\(\Leftrightarrow x=\frac{2}{3}\)
\(b.||3x+2|-2x-5|=3x-\left(-1\right)^{2015}\)
\(\Leftrightarrow||3x+2|-2x-5|=3x+1\)
\(\Leftrightarrow\orbr{\begin{cases}|3x+2|-2x-5=3x+1\\|3x+2|-2x-5=-3x-1\end{cases}\Leftrightarrow\orbr{\begin{cases}|3x+2|=5x+6\left(n\right)\\|3x+2|=-\left(x-4\right)\left(l\right)\end{cases}}}\)
\(\Leftrightarrow\orbr{\begin{cases}3x+2=5x+6\\3x+2=-5x-6\end{cases}\Leftrightarrow\orbr{\begin{cases}-2x=4\\8x=-8\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-2\\x=-1\end{cases}}}\)
V...\(x=-1;x=-2\)
x là -1; quá ư đơn giản
\(\Rightarrow\)3 (3x-2) = -5 (1-2x)
\(\Rightarrow\)9x-6 = -5+10x
\(\Rightarrow\)-6+5 = 10x-9x
\(\Rightarrow\)-1 = x
Vậy x = -1