Question

[Sửu Nhi]

a) |x-3|=|4-x|

b) |2x-1|+5=5

c) |x-1|(-1/2)^3=(-1 /2)^5

d) 3x-|2x+1|=2

e) |x|+|-x|=3-x

Answer 1

[Hoàng Lê Bảo Ngọc]

a/ \(\left|x-3\right|=\left|4-x\right|\) \(\Rightarrow\left[\begin{matrix}x-3=4-x\\x-3=x-4\end{matrix}\right.\) => x = \(\frac{7}{2}\)

b/ \(\left|2x-1\right|+5=5\Rightarrow\left|2x-1\right|=0\Rightarrow x=\frac{1}{2}\)

c/ \(\left|x-1\right|.\left(-\frac{1}{2}\right)^3=\left(-\frac{1}{2}\right)^5\)

\(\Rightarrow\left|x-1\right|=\left(-\frac{1}{2}\right)^5:\left(-\frac{1}{2}\right)^3\)

\(\Rightarrow\left|x-1\right|=\frac{1}{4}\)

\(\Rightarrow x-1=\pm\frac{1}{4}\)

\(\Rightarrow\left[\begin{matrix}x=\frac{5}{4}\\x=\frac{3}{4}\end{matrix}\right.\)

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

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

\(\Rightarrow x=3\) (loại x = 1/5)

e/ \(\left|x\right|+\left|-x\right|=3-x\)

Xét với x = 0 không thỏa mãn

Xét với x < 0 thì : (-x) + (-x) = 3 - x => x = -3

Xét với x > 0 thì : x + x = 3 - x => x = 1

Vậy x = 1 hoặc x = -3