Question

Tìm x.

A, |x|<1

B, |x+3|=0

C, |x+2|=|12-10|

D, |x+3|=2x-2

E, |x+1|>4

F, |x-3|=|2x-1|

G, |2x-1|-1+2x=0

H, |3-2x|=2x-3

J, |x+1 |+ |x+2| + |x+3|+|x+4|=5x

Bài này hơi dài, ai làm hết đc thì làm hộ mình, ko thì mỗi người một câu thôi. Mình cảm ơn

Answer 1

a) \(\left|x\right|< 1\Rightarrow-1< x< 1\Rightarrow x=0\)

b) \(\left|x+3\right|=0\)

\(\Leftrightarrow x+3=0\)

\(\Leftrightarrow x=-3\)

c) \(\left|x+2\right|=\left|12-10\right|\)

\(\Leftrightarrow\left|x+2\right|=2\)

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=0\end{matrix}\right.\)

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

\(\Leftrightarrow\left\{{}\begin{matrix}2x-2\ge0\\\left[{}\begin{matrix}x+3=2x-2\\x+3=\left(-2x\right)+2\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x\ge2\\\left[{}\begin{matrix}x-2x=-2-3\\x-\left(-2x\right)=2-3\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\\left[{}\begin{matrix}-x=-5\\3x=-1\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\\left[{}\begin{matrix}x=5\left(tm\right)\\x=\dfrac{-1}{3}\end{matrix}\right.\end{matrix}\right.\)

Vì \(\dfrac{-1}{3}< 1\) nên \(x=5\) thỏa mãn đề bài.

e) \(\left|x+1\right|>4\)

\(\Rightarrow\left[{}\begin{matrix}x+1>4\\x+1< 4\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x>3\\x< 3\end{matrix}\right.\)

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

(cho thời gian suy nghĩ, mình chưa làm dạng này bao giờ)

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

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

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

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

\(\Rightarrow-2x+1\ge0\)

\(\Rightarrow-2x\ge-1\)

\(\Rightarrow x\ge\dfrac{-1}{-2}=\dfrac{1}{2}\)

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

\(\Leftrightarrow\left\{{}\begin{matrix}2x-3\ge0\\\left[{}\begin{matrix}3-2x=2x-3\\3-2x=-2x+3\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x\ge3\\\left[{}\begin{matrix}3+3=2x+2x\\3-3=-2x+2x\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{3}{2}\\\left[{}\begin{matrix}6=4x\\0=0\end{matrix}\right.\end{matrix}\right.\)

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

Vì \(0=0\) luôn đúng nên ta có \(x=\dfrac{3}{2}\)

j) \(\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+\left|x+4\right|=5x\)

(đầu hàng)