\(x\in\left\{1;\dfrac{1}{2}\right\}\)

     \(2x\left(x-1\right)-x+1=0.\)

\(\Leftrightarrow2x\left(x-1\right)-\left(x-1\right)=0.\)

\(\Leftrightarrow\left(2x-1\right)\left(x-1\right)=0.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}.\\x=1.\end{matrix}\right.\)

Vậy \(x\in\left\{\dfrac{1}{2};1\right\}\) là nghiệm của phương trình trên.

\(a,2^{x+1}=32\\ 2^{x+1}=2^5\\ x+1=5\\ x=4\\ b,2^{2x}+2^{2x+1}=48\\ 2^{2x}+2\cdot2^{2x}=48\\ 3\cdot2^{2x}=48\\ 2^{2x}=16\\ 2^{2x}=2^4\\ 2x=4\\ x=2\)

\(c,3^x+5\cdot3^{x+1}=144\\ 3^x+15\cdot3^x=144\\ 16\cdot3^x=144\\ 3^x=9\\ 3^x=3^2\\ x=2\\ d,3^{x+5}=9^{x+1}\\ 3^{x+5}=3^{2x+2}\\ x+5=2x+2\\ x=3\)

 2x² - x  - 2x² - 3x + 4x + 6 

x = 6

a]={23;24;25;26....;35}

b]={4;8;14;...}

c]{4}

Tim x thuoc N=thi ko biet nha!

\(|x-1|=2x-5\)

\(\Rightarrow\hept{\begin{cases}x-1=2x-5\\x-1=5-2x\end{cases}}\)khi\(\hept{\begin{cases}x\ge1\\x\le1\end{cases}}\)

TH1: x\(\ge\)1

\(\Rightarrow x-1=2x-5\)

\(\Rightarrow x-2x=-5+1\)

\(\Rightarrow-x=-4\Rightarrow x=4\left(tm\right)\)

TH2 : x\(\le\)1

\(\Rightarrow x-1=5-2x\)

\(\Rightarrow x+2x=5+1\)

\(\Rightarrow3x=6\Rightarrow x=2\left(L\right)\)

Vậy x=4

Vì /x-1/ = 2x - 5 => x-1 = 2x-5 hoặc x-1 = -(2x-5)

Trường hợp 1:

x-1 = 2x-5

x-2x = -5 + 1

x.(1-2)= -4

-x = -4

=> x = 4

Trường hợp 2:

x -1 = -(2x - 5)

x -1 = -2x+5

x+2x = 5+1

3x = 6

x = 6:3

x=2

Vậy x = 4 hoặc x=2

Học tốt nha bn

\(|x-1|=2x-5\)

Ta có:\(|x-1|\ge0\Rightarrow2x-5\ge0\Rightarrow2x\ge5\Rightarrow x\ge\frac{5}{2}\)

\(TH1:x-1=2x-5\)

\(\Rightarrow-1+5=2x-x\)

\(\Rightarrow4=x\left(TM\right)\)

\(TH2:x-1=-\left(2x-5\right)\)

\(\Rightarrow x-1=-2x+5\)

\(\Rightarrow x+2x=1+5\)

\(\Rightarrow3x=6\Rightarrow x=2< \frac{5}{2}\left(KTM\right)\)

Vậy\(x=4\)

Bài 1:

Ta có: \(4-2\left(x+1\right)=2\)

\(\Leftrightarrow2\left(x+1\right)=2\)

\(\Leftrightarrow x+1=1\)

hay x=0

Bài 2: 

Ta có: \(\left|2x-3\right|-1=2\)

\(\Leftrightarrow\left|2x-3\right|=3\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-3=3\\2x-3=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)

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