<=>|x+1|=|x²+1|

=>|x+1=|x+1|*|x|

=>|x+1|-|x+1|=|x|

=>|x|=0 hay x=0

a) \(\left|\left|x-1\right|-1\right|=2\Rightarrow\orbr{\begin{cases}\left|x-1\right|-1=2\\\left|x-1\right|-1=-2\end{cases}}\Rightarrow\orbr{\begin{cases}\left|x-1\right|=3\\\left|x-1\right|=-1\left(l\right)\end{cases}}\)

TH1: x - 1 = 3

         x      = 4

TH2: x - 1 = - 3

        x       = - 2 

b) Tương tự câu a.

c) \(\left|\left|2x-3\right|-x+1\right|=42-8\)

\(\left|\left|2x-3\right|-x+1\right|=34\)

TH1: \(\left|2x-3\right|-x+1=34\)

\(\left|2x-3\right|-x=33\)

Với \(x\ge\frac{3}{2}\), ta có \(2x-3-x=33\Rightarrow x=36\)  (tm)

Với \(x< \frac{3}{2}\), ta có \(3-2x-x+1=34\Rightarrow-3x=30\Rightarrow x=-10\left(tm\right)\)

TH2: \(\left|2x-3\right|-x+1=-34\)

\(\left|2x-3\right|-x=-35\)

Với \(x\ge\frac{3}{2}\), ta có \(2x-3-x=-35\Rightarrow x=-32\)  (l)

Với \(x< \frac{3}{2}\), ta có \(3-2x-x+1=-34\Rightarrow-3x=38\Rightarrow x=\frac{38}{3}\left(l\right)\)

d) Tương tự câu c.

a: \(\Leftrightarrow\left\{{}\begin{matrix}3x-2>-4\\3x-2< 4\end{matrix}\right.\Leftrightarrow-\dfrac{2}{3}< x< 2\)

c: \(\Leftrightarrow\left[{}\begin{matrix}3x-1>5\\3x-1< -5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>2\\x< -\dfrac{4}{3}\end{matrix}\right.\)

d: \(\Leftrightarrow\left[{}\begin{matrix}3x+1>x-2\\3x+1< -x+2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x>-3\\4x< 1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>-\dfrac{3}{2}\\x< \dfrac{1}{4}\end{matrix}\right.\)

A, bạn ơi mình biết làm hết r

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\(2+\left(-1\right)1+\left(-3+1\right)x+x^2=0\)

\(2+\left(-1\right)0+\left(-1\right)+1\left(-3+1\right)x+x^2=0\)

\(x^2+\left(1-3\right)x-1+2=0\)

Sai k chju trắc nhiêm đâu nha

de

=>|2x+1|=|x-1|

=>2x+1=x-1 hoặc 2x+1=1-x

=>x=-2 hoặc x=0

`|2x+1|-|x-1|=0`

`<=>|2x+1|=|x-1|`

`<=>4x^2+4x+1=x^2-2x+1`

`<=>3x^2+6x=0`

`<=>3x(x+2)=0`

`<=>` $\left[\begin{matrix} x=0\\ x=-2\end{matrix}\right.$

\(\left|2x+1\right|-\left|x-1\right|=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}-x-1=1\\3x-1=-1\end{matrix}\right.\)

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

|x-1|+1=2013.

=>|x-1|=2012.

=>x-1E{-2012;2012}.

=>xE{-2011;2013}(tương ứng).

tk ek nha em mới lớp 6.

-chúc ai tk mk/em học giỏi và may mắn-

\(|x-1|+1=2013\Leftrightarrow|x-1|=2013-1=2012\Leftrightarrow\orbr{\begin{cases}x-1=-2012\\x-1=2012\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-2011\\x=2013\end{cases}}}\)