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. 1,7

b.3/7

a ) Vì | x + 1 | ≥ 0 ∀ x ∈ N 

Để A = | x + 1 | + 1,7 min <=> x + 1 = 0 => x = - 1

Vậy min A = 1,7 <=> x = - 1

b ) Vì B = | x - 2/3 | ≥ 0 ∀ x ∈ N 

Để | x -2/3 | + 3/7 min <=> x - 2/3 = 0 => x = 2/3

Vậy min B = 3/7 <=> x = 2/3