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|3\(x\) - 1| +|1 - 3\(x\)| = 9
vì |3\(x\) - 1| = |1 - 3\(x\)| nên:
|3\(x\) - 1| + |1 - 3\(x\)| = |3\(x\) - 1| + |3\(x\) - 1| = 2|3\(\)\(x\) - 1|
⇒2.|3\(x\) - 1| = 9
|3\(x\) - 1| = \(\dfrac{9}{2}\)
\(\left[{}\begin{matrix}3x-1=\dfrac{-9}{2}\\3x-1=\dfrac{9}{2}\end{matrix}\right.\)
\(\left[{}\begin{matrix}3x=-\dfrac{9}{2}+1\\3x=\dfrac{9}{2}+1\end{matrix}\right.\)
\(\left[{}\begin{matrix}3x=-\dfrac{7}{2}\\3x=\dfrac{11}{2}\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=-\dfrac{7}{6}\\x=\dfrac{11}{6}\end{matrix}\right.\)
Vậy \(x\) \(\in\) {- \(\dfrac{7}{6}\); \(\dfrac{11}{6}\)}
\(3x+3x+1+3x+2=117\)
\(\Rightarrow\left(3x+3x+3x\right)+\left(1+2\right)=117\)
\(\Rightarrow9x+3=117\)
\(\Rightarrow9x=117-3\)
\(\Rightarrow9x=114\)
\(\Rightarrow x=114:9\)
\(\Rightarrow x=\frac{38}{3}\)
Vậy \(x=\frac{38}{3}\)
P/s : Đúng nha
~ Ủng hộ nhé
|3x-1|+|3x-1|=6
2.|3x-1|=6
|3x-1|=3
=> 3x-1=3 hoặc 3x-1=-3
=> 3x =4 hoặc 3x=-2
=> x=4/3 hoặc x=-2/3
\(\left|3x-1\right|+\left|1-3x\right|=6\)
\(\Leftrightarrow\left|3x-1\right|+\left|3x-1\right|=6\)
\(\Leftrightarrow2\left|3x-1\right|=6\)
\(\Leftrightarrow\left|3x-1\right|=3\)
\(\Leftrightarrow\orbr{\begin{cases}3x-1=3\\3x-1=-3\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{4}{3}\\x=-\frac{2}{3}\end{cases}}\)
\(b.\) \(\left|3x-1\right|=6\)
\(\Leftrightarrow\orbr{\begin{cases}3x-1=6\\3x-1=-6\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}3x=6+1\\3x=-6+1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}3x=7\\3x=-5\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=7:3\\x=-5:3\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{7}{3}\\x=-\frac{5}{3}\end{cases}}\)
Vậy: \(x\in\left\{\frac{7}{3};-\frac{5}{3}\right\}\)
\(a.\) \(\left|3x-1\right|=0\)
\(\Leftrightarrow3x-1=0\)
\(\Leftrightarrow3x=0+1\)
\(\Leftrightarrow3x=1\)
\(\Leftrightarrow x=1:3\)
\(\Leftrightarrow x=\frac{1}{3}\)
Vậy: \(x=\frac{1}{3}\)
a,
\(|3x-1|=0\)
\(\Rightarrow3x-1=0\)
\(3x=1\)
\(x=\frac{1}{3}\)
a,
|3x-1|=0
=>3x-1=0
3x=0+1
3x=1
x=1/3
b,
|3x-1|=6
=>3x-1=6 hoặc 3x-1=-6
Trường hợp 1:
3x-1=6
3x=6+1
3x=7
3x=7/3
Tường hợp 2:
3x-1=-6
3x=-6+1
3x=-5
x=-5/3
c, Hơi dài nên ở bài sau
\(a,\Rightarrow x\in\varnothing\left(\left|4+2x\right|\ge0>-4\right)\\ b,\Rightarrow\left|3x-1\right|=x-2\\ \Rightarrow\left[{}\begin{matrix}3x-1=x-2\left(x\ge\dfrac{1}{3}\right)\\3x-1=2-x\left(x< \dfrac{1}{3}\right)\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\left(ktm\right)\\x=\dfrac{3}{4}\left(ktm\right)\end{matrix}\right.\\ \Rightarrow x\in\varnothing\\ c,\Rightarrow\left|x+15\right|=3x-1\\ \Rightarrow\left[{}\begin{matrix}x+15=3x-1\left(x\ge-15\right)\\x+15=1-3x\left(x< -15\right)\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=8\left(tm\right)\\x=-\dfrac{7}{2}\left(ktm\right)\end{matrix}\right.\\ \Rightarrow x=8\)
\(2\cdot3^x-405=3^{x-1}\\\Rightarrow2\cdot3^x-3^{x-1}=405\\\Rightarrow2\cdot3^x-3^x\cdot3^{-1}=405\\\Rightarrow3^x\cdot(2-3^{-1})=405\\\Rightarrow3^x\cdot(2-\frac13)=405\\\Rightarrow3^x\cdot\frac53=405\\\Rightarrow3^x=405:\frac53\\\Rightarrow3^x=243\\\Rightarrow3^x=3^5\\\Rightarrow x=5\)
\(\left(3x-1\right)^6=\left(3x-1\right)^4\\ =>\left(3x-1\right)^6-\left(3x-1\right)^4=0\\ =>\left(3x-1\right)^4\left[\left(3x-1\right)^2-1\right]=0\\ =>\left[{}\begin{matrix}\left(3x-1\right)^4=0\\\left(3x-1\right)^2-1=0\end{matrix}\right.=>\left[{}\begin{matrix}\left(3x-1\right)=0\\3x-1=1\\3x-1=-1\end{matrix}\right.=>\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=\dfrac{2}{3}\\x=0\end{matrix}\right.\)