exercices 6 résous les équations suivantes. a) x sur 2 =4 sur 3 B) 3x sur 5 = 4 sur 7 C) 5a sur 4 = 3 sur 2 d) 3 sur 2x- 1 sur 2 = 5 sur 6 e) 5 sur 2 x=5 sur 4x

bonjour,

a) x/2 = 4/3

• x/2 × 2 = 4/3 × 2

• x = 8/3 ✅

b) 3x/5 = 4/7

• 3x/5 × 5 = 4/7 × 5

• 3x = 20/7

• 3x ÷ 3 = 20/7 ÷ 3

• x = 20/7 × 1/3 = 20/21 ✅

c) 5a/4 = 3/2

• 5a/4 × 4 = 3/2 × 4

• 5a = 12/2

• 5a = 6

• 5a/5 = 6/5

• a = 6/5 ✅

d) 3/(2x - 1) / 2 = 5/6

• 3/(2x - 1) × 1/2 = 5/6

• 3/(4x - 2) = 5/6

• 3 = 5/6 × (4x - 2)

• 3 = 5(4x - 2) / 6

• 3 = (20x - 10) / 6

• 3 × 6 = 20x - 10

• 20x - 10 = 18

• 20x = 28

• x = 28/20 = 14/10 = 7/5 ✅

e) 5/2x = 5/(4x + 3) / 3

• 5/2x × 3 = 5/(4x + 3)

• 15/2x = 5/(4x + 3)

• 15/2x × (4x + 3) = 5

• (60x + 45) / 2x = 5

• 60x + 45 = 10x

• 50x = -45

• x = -45/50 = -9/10 ✅

Bonne journée !

bonjour

x /2 = 4 /3

   3 x /6 = 8/6

   3 x = 8

      x = 8/3

b ) 3 x /5 = 4 /7

    21 x /35 = 20/35

    21 x = 20

      x = 20/21

c )  5 a/4 = 3 /2

     5 a /4 = 6/4

      5 a = 6

      a = 6/5

d)  3  /( 2 x - 1 ) / 2 = 5 /6

    3 / ( 2 x - 1 ) * 1/2 = 5 /6

    3 / ( 4 x - 2 ) = 5/6

    3 = 5/6 ( 4 x - 2 )

    3  = ( 20 x - 10 ) / 6

    3  *6  = 20 x - 10

    18  + 10 = 20 x

    - 20 x = - 28

    x = - 28 / - 20 =  28/20 = 7/5

e) 5/ 2x = 5/(4x + 3) / 3

5/2x * 3 = 5/(4x + 3)

15/2x = 5/(4x + 3)

15/2x  (4x + 3) = 5

(60x + 45) / 2x = 5

60x + 45 = 10x

60 x - 10 x = - 45

50 x = - 45

x = - 45/50 = - 9/10