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B, => 2x+5=3x-8
2x-3x=-8-5
-x=-13
=>x=13
hoặc 2x+5=-3x+8
2x+3x=8-5
5x=3
x=\(\frac{3}{5}\)
\(\left|x+1\right|+\left|x-5\right|=7.\)
\(Th1:x+1< 0;x-5< 0\)
\(x< -1;x< 5\Rightarrow x< -1\)
\(\left|x+1\right|+\left|x-5\right|=7\)
\(-\left(x+1\right)-\left(x-5\right)=7\)
\(-x-1-x+5=7\)
\(-2x+4=7\)
\(-2x=3\)
\(x=-1,5\left(tm\right)\)
\(Th2:x+1>0;x-5>0\)
\(x>-1;x>5\Rightarrow x>5\)
\(\left|x+1\right|+\left|x-5\right|=7\)
\(x+1+x-5=7\)
\(2x-4=7\)
\(2x=11\)
\(x=5,5\)\(\left(tm\right)\)
\(Th3:x+1\le0;x-5>0\)
\(x\le-1;x>5\)(không xảy ra)
\(Th4:x+1>0;x-5\le0\)
\(x>-1;x\le5\Rightarrow-1< x\le5\)
\(\left|x+1\right|+\left|x-5\right|=7\)
\(-\left(x+1\right)+x-5=7\)
\(-x-1+x-5=7\)( không xảy ra)
Vậy x = -1,5 hoặc x = 5,5
\(\)
c) |2x + 3| - 4x < 9
Xét x ≥ -3/2
=> |2x + 3| - 4x < 9
<=> 2x + 3 - 4x < 9
<=> - 2x + 3 < 9
=> - 2x < 6
=> x < - 3
Xét x < -3/2 tương tự
b,xet 2 TH
TH1 3x-5=x+2
=>3x-x=2+5
=>2x=7
=>x=7/2
TH2 5-3x=x+2
=>-3x-x=5-2
=>-2x=3
=>x=-3/2
THẤY ĐÚNG THÌ
THANK
Ta có : \(\left(2x+3\right)\left(x-7\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x+3=0\\x-7=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x=-3\\x=7\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-\frac{3}{2}\\x=7\end{cases}}\)
a) \(\Leftrightarrow\left|2x-3\right|=\frac{1}{4}\Leftrightarrow\orbr{\begin{cases}x\ge\frac{3}{2}\mid:2x-3=\frac{1}{4}\Rightarrow2x=\frac{13}{4}\Rightarrow x=\frac{13}{8}\left(TM\right)\\x< \frac{3}{2}\mid:3-2x=\frac{1}{4}\Rightarrow2x=\frac{11}{4}\Rightarrow x=\frac{11}{8}\left(TM\right)\end{cases}.}\)
b) \(\Leftrightarrow\left|x-1\right|=\frac{3}{4}\Leftrightarrow\orbr{\begin{cases}x\ge1\mid:x-1=\frac{3}{4}\Rightarrow x=\frac{7}{4}\left(TM\right)\\x< 1\mid:1-x=\frac{3}{4}=>x=\frac{1}{4}\left(TM\right)\end{cases}}\)
c) \(\frac{3}{5\left(x-\frac{5}{6}\right)}-\frac{1}{2\left(\frac{3}{2}-1\right)}=-\frac{1}{4}\Leftrightarrow\frac{3}{\frac{5\left(6x-5\right)}{6}}-\frac{1}{2\cdot\frac{1}{2}}=-\frac{1}{4}\Leftrightarrow\frac{18}{5\left(6x-5\right)}=-\frac{1}{4}+1\)
\(\Leftrightarrow\frac{18}{5\left(6x-5\right)}=\frac{3}{4}\Leftrightarrow6x-5=\frac{24}{5}\Leftrightarrow6x=\frac{49}{5}\Leftrightarrow x=\frac{49}{30}\)
d) \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2016}\)
\(\Leftrightarrow\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\frac{2}{4\cdot5}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2016}\)
\(\Leftrightarrow2\cdot\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2015}{2016}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2015}{2016}\Leftrightarrow2\cdot\frac{x+1-2}{2\left(x+1\right)}=\frac{2015}{2016}\Leftrightarrow\frac{x-1}{x+1}=\frac{2015}{2016}\)
\(\Leftrightarrow2016x-2016=2015x+2015\Leftrightarrow x=2015+2016=4031\)
Vậy x = 4031.
\(2\left(|x-1|+x-\frac{4}{5}\right)=2x-\frac{2}{5}\)
\(TH1:x\ge1\Rightarrow|x-1|=x-1\)
\(\Rightarrow2\left(x-1+x-\frac{4}{5}\right)=2x-\frac{2}{5}\)
\(\Rightarrow2\left(2x-\frac{9}{5}\right)=2x-\frac{2}{5}\Rightarrow4x-\frac{18}{5}=2x-\frac{2}{5}\)
\(\Rightarrow4x-2x=\frac{18}{5}-\frac{2}{5}\Rightarrow2x=\frac{16}{5}\Rightarrow x=\frac{16}{5}:2=\frac{16}{10}=\frac{8}{5}\)
\(TH2:x< 1\Rightarrow|x-1|=-x+1\)
\(\Rightarrow2\left(-x+1+x-\frac{4}{5}\right)=2x-\frac{2}{5}\)
\(\Rightarrow2\left(1-\frac{4}{5}\right)=2x-\frac{2}{5}\Rightarrow2\cdot\frac{1}{5}=2x-\frac{2}{5}\)
\(\Rightarrow2x-\frac{2}{5}=\frac{2}{5}\Rightarrow2x=\frac{2}{5}+\frac{2}{5}=\frac{4}{5}\Rightarrow x=\frac{4}{5}:2=\frac{4}{10}=\frac{2}{5}\)
a) |x|=5
\(\Rightarrow\)x=5 hoặc x=-5
Vậy x=5 hoặc x=-5
b)|2x-1|=7
TH1: 2x-1=7
2x=7+1
2x=8
x=4
TH2:2x-1=-8
2x=-8+1
2x=-7
x=-7:2
x=-7/2
Vậy x= -7/2 hoặc x=4
a - x = 5 hoặc -5
b- =
th1 : 2x = 7+1
2x = 8
x= 8:2
x =4
th2 : 2x = -7 +1
2x = -6
x = -6 : 2
x = -3