Question

Tìm x biết:

a. /4x+3/-x=15

b. /3x-2/-x >1

c./2x+3/ bé hơn hoặc bằng 5

Answer 1

a) \(\left|4x+3\right|-x=15\)

\(\Rightarrow\left|4x+3\right|=15+x\)

\(\Rightarrow\left[{}\begin{matrix}4x+3=15+x\\4x+3=-15+x\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}4x-x=15-3\\4x-x=-15-3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}3x=12\\3x=-18\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-6\end{matrix}\right.\)

b) \(A=\left|3x-2\right|\)

Dấu = xảy ra khi \(3x-2=0\)

\(\Rightarrow3x=2\Rightarrow x=\dfrac{2}{3}\)

A_min = 1 <=> x = 2/3

c) \(B=\left|2x+3\right|\le5\)

Dấu = xảy ra <=> 2x + 3 = 0 => 2x = -3 => x = -3/2

B_max = 5 <=> x = -3/2