Question

Tìm x, biết :

a. \(\left|x+1\right|-4=0\)

b. \(\left|x-5\right|+15-x=0\)

c.\(3x+\left|2x\right|=5x\)

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

Answer 1

a, \(\left|x+1\right|-4=0\)

\(\Rightarrow\left|x+1\right|=4\)

+) Xét \(x\ge-1\) có:

\(x+1=4\Rightarrow x=3\) ( t/m )

+) Xét x < -1 có:

\(-x-1=4\Rightarrow x=-5\) ( t/m )

Vậy x = 3 hoặc x = -5

b, tương tự

c, \(3x+\left|2x\right|=5x\)

\(\Rightarrow\left|2x\right|=2x\)

+) Xét \(x\ge0\)

\(\Rightarrow2x=2x\Rightarrow x\in R\forall x>0\)

+) Xét x < 0

\(\Rightarrow-2x=2x\Rightarrow x=0\)

Vậy \(x\ge0\)

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

\(\Rightarrow\left[{}\begin{matrix}2x+1=x-3\\2x+1=3-x\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-4\\x=\dfrac{2}{3}\end{matrix}\right.\)

Vậy...