Question

[Phạm Minh Quân]

Tìm x biết

/10x+7/<37

/3-8x/ =< 19

/x+3/-2x=/x-4/

Answer 1

[Kirigawa Kazuto]

a) |10x + 7| < 37

=> -37 < 10x + 7 < 37

=> -44 < 10x < 30

=> -4,4 < x < 3

b) |3 - 8x| \(\le\)19

=> -19 \(\le\) 3 - 8x \(\le\) 19

=> -22 \(\le\) -8x \(\le\) 16

=> 2,75 \(\le\) x \(\le\) -2

=> x không có giá trị thõa mãn

Answer 2

[qwerty]

c) \(\left|x+3\right|-2x=\left|x-4\right|\)

\(\Rightarrow\left|x+3\right|-2x-\left|x-4\right|=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+3-2x-\left(x-4\right)=0\left(đk:x+3\ge0,x-4\ge0\right)\\-\left(x+3\right)-2x-\left(x-4\right)=0\left(đk:x+3< 0,x-4\ge0\right)\\x+3-2x-\left(-\left(x-4\right)\right)=0\left(đk:x+3\ge0,x-4< 0\right)\\-\left(x+3\right)-2x-\left(-\left(x-4\right)\right)=0\left(đk:x+3< 0,x-4< 0\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\left(đk:x\ge-3;x\ge4\right)\\x=\dfrac{1}{4}\left(đk:x< -3,x\ge4\right)\\x\in\varnothing\left(đk:x\ge-3,x< 4\right)\\x=-\dfrac{7}{2}\left(đk:x< -3;x< 4\right)\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x\in\varnothing\\x\in\varnothing\\x\in\varnothing\\x=-\dfrac{7}{2}\end{matrix}\right.\)

Vậy \(x=-\dfrac{7}{2}\)