CORRIGES:

EXERCICE I.

1)

a) < = >3x=13x5 => x=65/3

b) -5x+2=3x+5 <=>-5x-3x=5-2 < = > -8x=3 => x=-3/8 =>S= {-3/8}

c) (2x-5)/3 =(x+1)/2< = >2(2x-5) =3(x+1) < = >4x-10=3x+3< = >4x-3x=3+10 =>x=13=>S= {13}

d) x(-x+5)=0  =>x=0 ou x=5 o=>S={0,5}

EXERCICE II .

a) |4x +5|=3 <=>(4x+5=3) ou (4x+5=-3) <=> x=-1/2 ou x=-2 => S= {-2,-1/2}

b) |2x-5|=|-x+3|<=> (2x -5=-(-x+3)) ou (2x-5=+(-x+3) =>x=2 ou x=8/3.

c) |x-5|=4<=>(x-5=-4) ou (x-5=4) => x=1 ou x=9 => S= {1,9}

d) |3x-1|<=>(3x-1=-4) ou (3x-1=4)   =>S= {-1,-3/5}

EXERCICE III:

1.Soit x le prix de cet article.

On a: ( 3/4 )x =x-150

 ( 3/4 )x = x-150 <=> ( 3/4 )x -x= <=>3x-4x=4(-150) <=>-x=-600 => x=600

2.soit x la longueur de ce Jardin. On a:

10=2x +4 < = >2x=10-4 =>x=3

De plus:

P (L+l)x2=2L+2l< = >10=2x3+2L =>l=2

3.

A=cxc=(x-4)(x-4)

A=3c < = >(x-4)(x-4)=3(x-4)

          < = >(x-4)(x-4)-3(x-4)=0 =>x=4 ou x=7

a)puisque x>5 alors x=7

b) c=x-4=7-4=3m