Question

Rezolvati ecuatiile

|x/6-1/2|+2/3=3

-7|x+3|=5|x+3|-6

Answer 1

|x/6-1/2|+2/3=3
|x/6-1/2|= {a)x/6-1/2 daca x/6-1/2$\geq$0
               {b)-x/6+1/2 daca x/6-1/2<0
a) (x/6-1/2)+2/3=3
    (x/6-3/6)+4/6=18/6
    x-3+4=18
    x=18+3-4
    x=17
b) (-x/6+1/2)+2/3=3
    (-x/6+3/6)+4/6=18/6
     -x+3+4=18
     -x=18-3-4
     -x=11*(-1)
      x= -11
-7|x+3|=5|x+3|-6
|x+3|= {x+3 daca x+3$\geq$0
          {-x-3 daca x+3<0
a) -7(x+3)=5(x+3)-6
   -7*x-7*3=5*x+5*3-6
   -7x-21=5x+15-6
   -7x-5x=15-6+21
   -12x=30*(-1)
       x=-30/12
       x=-5/2
b)-7(-x-3)=5(x+3)-6
   -7*(-x)-7*(-3)=5*x+5*3-6
   7x+21=5x+15-6
   7x-5x= -21+15-6
   2x= -12
     x= -12/2
     x= -6
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