Question

Rút gọn biểu thức: \(E=3.\left|x-1\right|+2.\left|x+3\right|\)

Answer 1

Lời giải:

Nếu $x\geq 1$: \(\left\{\begin{matrix} |x-1|=x-1\\ |x+3|=x+3\end{matrix}\right.\). Khi đó:

$E=3|x-1|+2|x+3|=3(x-1)+2(x+3)=5x+3$

Nếu $-3\leq x< 1$: \(\left\{\begin{matrix} |x-1|=1-x\\ |x+3|=x+3\end{matrix}\right.\). Khi đó:

$E=3(1-x)+2(x+3)=-x+9$

Nếu $x< -3$: \(\left\{\begin{matrix} |x-1|=1-x\\ |x+3|=-x-3\end{matrix}\right.\). Khi đó:

$E=3(1-x)+2(-x-3)=-5x-3$

Answer 2

Lời giải:

Nếu $x\geq 1$: \(\left\{\begin{matrix} |x-1|=x-1\\ |x+3|=x+3\end{matrix}\right.\). Khi đó:

$E=3|x-1|+2|x+3|=3(x-1)+2(x+3)=5x+3$

Nếu $-3\leq x< 1$: \(\left\{\begin{matrix} |x-1|=1-x\\ |x+3|=x+3\end{matrix}\right.\). Khi đó:

$E=3(1-x)+2(x+3)=-x+9$

Nếu $x< -3$: \(\left\{\begin{matrix} |x-1|=1-x\\ |x+3|=-x-3\end{matrix}\right.\). Khi đó:

$E=3(1-x)+2(-x-3)=-5x-3$