Question

b/ / 4-2x/ +/2x-2/ =7

Answer 1

+ Với x < 1 thì |4 - 2x| = 4 - 2x; |2x - 2| = 2 - 2x

Ta có: (4 - 2x) + (2 - 2x) = 7

=> 4 - 2x + 2 - 2x = 7

=> 6 - 4x = 7

=> 4x = 6 - 7

=> 4x = -1

=> \(x=\frac{-1}{4}\), thỏa mãn x < 1

+ Với \(1\le x\le2\) thì |4 - 2x| = 4 - 2x; |2x - 2| = 2x - 2

Ta có: (4 - 2x) + (2x - 2) = 7

=> 4 - 2x + 2x - 2 = 7

=> 2 = 7, vô lý

+ Với 2 < x thì |4 - 2x| = 2x - 4; |2x - 2| = 2x - 2

Ta có: (2x - 4) + (2x - 2) = 7

=> 2x - 4 + 2x - 2 = 7

=> 4x - 6 = 7

=> 4x = 7 + 6

=> 4x = 13

=> \(x=\frac{13}{4}\), thỏa mãn x > 2

Vậy \(\left[\begin{array}{nghiempt}x=\frac{-1}{4}\\x=\frac{13}{4}\end{array}\right.\)

Answer 2

TH1: \(x\le1\)

<=>4-2x+2-2x=7<=>6-4x=7<=>4x=-1<=>\(x=-\frac{1}{4}\)(tmđk \(x\le1\))

TH2: \(1< x\le2\)

<=>4-2x+2x-2=7<=>2=7 vô lý!

TH3:x>2

<=>2x-4+2x-2=7<=>4x-6=7<=>4x=13<=>\(x=\frac{13}{4}\)(tmđk x>2)

Vậy \(x=-\frac{1}{4}\) hoặc \(x=\frac{13}{4}\)