Question

Resolva as inadequações abaixo U=N


A) 7x-9<2x+16
B)2(3x+7) <-4+8
C) -(8-4x-7)<2x+7
D) 20-2(3x+4)+2(3-7x)>2(-x+5)-7x+9
E) 8x-10>2x+8

Answer 1

         Conjunto  N = {0,1,2,3,4,5,...} ***números inteiros positivos
 
               A) 7x - 9 < 2x +16
                    7x - 2x < 16 + 9
                           5x < 25
                             x <  5
                                           S = {0,1,2,3,4}

       B) 2(3x + 7) < -4 + 8
           6x + 14  <  4
                   6x  < 4 - 14
                   6x  < - 10
                     x  < -10/6
                     x  < - 5/2 <-- não pertence ao conjunto N
        S = {Ф}

     C)  - (8-4x-7) < 2x + 7
           -8+4x+7  < 2x + 7
              4x - 2x < 7 - 7 + 8   
                     2x < 8
                       x < 4
                                        S = {0,1,2,3}

    D) 20-2(3x+4)+2(3-7x) > 2(-x+5) -7x+9
        20 - 6x - 8 + 6 - 14x > -2x + 10 -7x + 9
                      - 20x + 18  > - 9x + 19
                      - 20x + 9x  > 19 - 18
                               - 11x >  1
                                 11x < -1
                                    x  < -1/11 <-- não pertence ao conjunto N
      S = {Ф}

    E) 8x-10 > 2x+8
         8x - 2x > 8 + 10
                6x > 18
                  x > 3
                                 S= {4,5,6,7,...}