giai phuong trinh a, l2x – 3l = 4 b, l3x – 1l – x = 2 c, lx – 7l = 2x + 3 d, lx – 4l + 3x = 5 e, lx – 7l = 2 g, l5 – 2xl – 1 = x giup minhh

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1.  

   Giải thích các bước giải:

    a,TH1: nếu 2x-3≥0→x≥0→|2x-3|=2x-3
   Ta có: 2x-3=4
           ⇔2x=7
           ⇔x=7/2(tm)
   vậy S={7/2}
   TH2:nếu 2x-3<0→|2x-3|=-2x+3
   ta có: -2x+3=4
       ⇔-2x=1
       ⇔x= 1/2(ktm)
   vậy S={∅}
   các câu còn lại làm tương tự bạn nhé!

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2. Đáp án:

    $a)| 2x-3| =4$

   Th1 :

   $2x-3 =4$

   $⇔2x = 7$

   $⇔x=\dfrac{7}{2}$

   Th2 :

   $2x-3 = -4$

   $⇔2x =-1$

   $⇔x=-\dfrac{1}{2}$

   $\text{Vậy S={$\dfrac{7}{2} ; -\dfrac{1}{2}$}}$

   $b) |3x -1| -x =2$

   $⇔|3x-1| =2+x$

   Th1 : $3x-1 ≥ 0 ⇔ x ≥ \dfrac{1}{3}$

   $⇔3x-1 =2+x$

   $⇔2x=3$

   $⇔x=\dfrac{3}{2}(TM)$

   Th2 :$3x-1 ≤ 0 ⇔ x ≤ \dfrac{1}{3}$

   $⇔3x-1 =-2-x$

   $⇔4x =-1$

   $⇔x=-\dfrac{1}{4}(TM)$

   $\text{Vậy S={$\dfrac{3}{2} ; -\dfrac{1}{4}$}}$

   $c) |x-7|=2x+3$

   Th1 : $x -7 ≥ 0 ⇔ x ≥ 7$

   $⇔x-7 =2x+3$

   $⇔-x= 10$

   $⇔x=-10 (KTM)$

   TH2 : $x-7 ≤ 0 ⇔ x ≤ 7$

   $⇔x-7 = -2x -3$

   $⇔3x=4$

   $⇔x=\dfrac{4}{3} (TM)$

   $\text{Vậy S={$\dfrac{4}{3}$}}$

   $d) |x-4| +3x=5$

   $⇔|x-4| = 5-3x$

   Th1 :$x-4 ≥ 0 ⇔ x ≥ 4$

   $⇔x-4 =5-3x$

   $⇔4x =9$

   $⇔x=\dfrac{9}{4}(KTM)$

   Th2  : $x-4 ≤ 0 ⇔ x ≤ 4$

   $⇔x-4= -5+3x$

   $⇔-2x=-1$

   $⇔x=\dfrac{1}{2}(TM)$

   $\text{Vậy S={$\dfrac{1}{2}$}}$

   $e) |x-7| =2$

   Th1 : $x-7 =2$

   $⇔x=9$

   Th2 : $x-7=-2$

   $⇔x=5$

   $\text{Vậy S={9 ; 5} }$

   $g) |5-2x| -1=x$

   $⇔|5-2x| =x+1$

   Th1 : $5-2x ≥ 0⇔x ≤ \dfrac{5}{2}$

   $⇔5-2x= x +1$

   $⇔-3x =-4$

   $⇔x=\dfrac{4}{3}(TM)$

   Th2 : $5-2x ≤ 0 ⇔ x ≥ \dfrac{5}{2}$

   $⇔5-2x =-x-1$

   $⇔-x=-6$

   $⇔x=6 (TM)$

   $\text{Vậy S={$\dfrac{4}{3}$ ; 6$}}$

    

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