Question

Tìm x

a ,\(\left|3-x\right|+2\cdot\left|7-x\right|=18\)

b , \(12-\left|5-x\right|=2x+7\)

c , \(3x\cdot\left|2x+3\right|-7x=x-8\)

Answer 1

a: =>|x-3|+2|x-7|=18(1)

Trường hợp 1: x<3

(1) trở thành 3-x+2(7-x)=18

=>3-x+14-2x=18

=>17-3x=18

=>3x=-1

hay x=-1/3(nhận)

Trường hợp 2: 3<=x<7

(1) trở thành x-3+2(7-x)=18

=>x-3+14-2x=18

=>11-x=18

hay x=-7(loại)

Trường hợp 3: x>=7

(1) trở thành x-3+2(x-7)=18

=>x-3+2x-14=18

=>3x-17=18

hay x=35/3(nhận)

b: =>12-|x-5|=2x+7

=>|x-5|=12-2x-7

=>|x-5|=-2x+5

\(\Leftrightarrow\left\{{}\begin{matrix}x< =\dfrac{5}{2}\\\left(-2x+5\right)^2=\left(x-5\right)^2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x< =\dfrac{5}{2}\\\left(2x-5-x+5\right)\left(2x-5+x-5\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x< =\dfrac{5}{2}\\x\cdot\left(3x-10\right)=0\end{matrix}\right.\Leftrightarrow x\in\left\{0;\dfrac{10}{3}\right\}\)