Réponse :
1) 3/2x - 5/3 = 0
3/2x = 5/3 x = (5/3)/(3/2) = (5/3) * (2/3) = 10/9
2) 2x + racine carrée de 3 = 0
x = racine carrée de 3/2
3) 3x - 5 = 1/2x 3x - 1/2x = 5 (3x*2)/(1*2) - 1/2x = 5 6x/2 - 1/2x = 5
5x/2 = 5 x = 5/(5/2) = 5 * 2/5 = 10/5 = 2
4) 2/3x + 1 = x - 3 2/3x - (3*x)/(3*1) = - 3 - 1 2/3x - 3x/3 = - 4
-x/3 = -4 x = 3*4 = 12
5) racine carrée de 2x + 1 /racine carrée de 2 = 0
x(racine carrée de 2) = 1/racine carrée de 2
x = 1/racine carrée de 2 /racine carrée de 2 = 1*racine carrée de 2/racine carrée de 2/1 = racine carrée de 2/racine carrée de 2 = 1
6) 2(x - 3) = 1/4(3x - 2) + 1/2 2x - 6 = 3/4x - 2/4 + 1/2
2x - 3/4x = - 2/4 + 1/2 + 6
(4*2x)/(4*1) - 3x/4 = -2/4 + (1*2)/(2*2) + (6*4)/(1*4)
8x/4 - 3x/4 = -2/4 + 2/4 + 24/4
5/4x = 24/4 x = 24/4 / 5/4 = 24/4 * 4/5 = 96/20 = 48/10 = 24/5
7) 2x - 3(x + 1) = (1 - 2x)/2
2x - 3x - 3 - (1 - 2x)/2 = 0 -x - 3 = (1 - 2x)/2
-x = (-2x + 1)/2 + 3 2(-1)x = 2[(-2x + 1)/2 + 3]
2(-1)x = 2(-2x+1)/2 + 2*3
2(-1)x = - 2x + 1 + 2*3
-2x = -2x + 1 + 2*3
-2x = - 2x + 1 + 6
-2x = -2x + 7
-2x + 2x = -2x + 7 + 2x
0 = 7 FAUX
10) (x+1)/2 + (x+2)/3 + (x+3)/4 = 12x - 1
6(x+1)/(6*2) + 4(x+2)/(4*3) + 3(x+3)/(3*4) = 12x - 1
(6x+6)/12 + (4x+8)/12 + (3x+9)/12 = 12x - 1
6x/12 + 6/12 + 4x /12 + 8/12 + 3x/12 + 9/12 = 12x - 1
13x/12 - 12x = -1 - 23/12
13x/12 - (12x*12)/(1*12) = (-1*12)/(1*12) - 23/12
13x/12 - 144x/12 = -24/12
-131x/12 = -24/12 x = -24/12 / -131/12 x = 24/12 * 12/131 = 288/1 572 = 96/524
Explications étape par étape
