Mathématiques

Question

Aidez moi a faire ces deux exos je n'ai pas très bien compris !! Merci bcp pr ceux qui m'aideront <<3

Exercice 1: Résoudre les équations suivantes:
a) 4x+11=2x+15         b) 3x+2=2x+5
c) 5x+3=x+11             d) 5x+5=3x+12
 
 Exercice 2: Résoudre les équations suivantes:
a)2(x-5)=3(-x+5)
b) -(-a+3)=5(3-a)+2
c) m-(5-2m)=3m-15

2 Réponse

  • Exercice 1:
    a) 4x+11=2x+15
       4x -2x = 15- 11
       2x = 4
         x = 2
    b) 3x+2=2x+5
        3x-2x = 5 - 2
           x = 3
    c) 5x+3=x+11
        5x -x = 11-3
       4x
    = 8
        x = 2
    d) 5x+5=3x+12
         5x -3x = 12-5
           2x= 7
            x = 7/2
    Exercice 2:
      
    ==> on développe, on simplifie puis on essaye de resoudre les equations :
    a) 2(x-5)=3(-x+5)  
      2x -10 = -3x + 15
       5x = 25
       x = 5
    b) -(-a+3)=5(3-a)+2
       a - 3 = 15 - 5a + 2
       6a = 20
         a = 20/6 = 10/3
     
    c) m-(5-2m)=3m-15  
    m-5 + 2m = 3m - 15
    6m = -10
    m = -10/6 = -5/3




  • Exercice 1:

    a) 4x + 11 = 2x + 15
    4x + 11 - 11 = 2x + 15 - 11
    4x = 2x + 3
    4x - 2x = 2x - 2x + 3
    2x = 3
    x = 3/2
    x = 1.5

    b) 3x + 2 = 2x + 5
    3x - 2x + 2 = 2x - 2x + 5
    x + 2 = 5
    x + 2 - 2 = 5 - 2
    x = 3

    c) 5x + 3 = x + 11
    5x - x + 3 = x - x + 11
    4x + 3 = 11
    4x + 3 - 3 = 11 - 3
    4x = 8
    x = 8/4
    x = 2

    d) 5x + 5 = 3x + 12
    5x - 3x + 5 = 3x - 3x + 12
    2x + 5 = 12
    2x + 5 - 5 = 12 - 5
    2x = 7
    x = 7/2


    Exercice 2 :

    a) 2 ( x - 5 ) = 3 (-x + 5 )
    2x - 10 = -3x + 15
    2x + 3x - 10 = -3x + 3x + 15
    5x + 10 = 15
    5x + 10 - 10 = 15 - 10
    5x = 5
    x = 5/5
    x = 1

    b) - (-a + 3) = 5 (3 - a) + 2
    a - 3 = 5x3 + 5 x (-a) + 2
    a - 3 = 15 - 5a + 2
    a - a - 3 = 15 - 5a - a + 2
    -3 = 15 - 6a + 2
    -3 = 15 +2 - 6a
    -3 = 17 - 6a
    -3 + 6a = 17 - 6a + 6a
    -3 + 6a = 17
    -3 + 3 + 6a = 17 + 3
    6a = 20
    a = 20/6
    a = 4

    c) m-(5-2m) = 3m - 15
    m - 5 + m + 2m = 3m - 15
    m + m + 2m - 5 = 3m - 15
    4m - 5 = 3m - 15
    4m - 3m - 5 = 3m - 3m - 15
    m - 5 = -15
    m - 5 + 5 = -15 + 5
    m = -10

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