Rezolvarea de ecuatii, inecuatii si rezolvarea problemelor cu ajutorul ecuatiilor

Exercitii:

1)      Verificati daca 3 este solutie pentru ecuatiile:

a)      5 + x = 8; x = 8 – 5; x = 3;

b)      x – 1 = 2; x = 2 + 1; x = 3;

c)      7 – x = 3; 7 – x – 3 =0; 4 – x = 0; x = 4;

d)      3 * x = 9; x = 9 : 3 ; x = 3;

e)      4 * x = 10; x = 10 : 4; x = 2.5;

f)       30 : x = 10; x = 30 : 10; x = 3;

g)      x : 3 = 2; x = 2 * 3; x = 6;

h)      5 + 4 (x – 1 ) = 5x – 2;

5 + 4x – 4 = 5x – 2;

5 + 4x – 4 – 5x + 2 = 0

3 – x = 0

X = 3;

i)        2 * [4 *( 7 – x ) – 5 * x ] + 6 = 8;

2 * ( 28 – 4x – 5x) + 6 = 8

56 – 8x – 10x + 6 – 8 = 0

54 – 18x = 0

54 = 18x

X = 3;

2)      Rezolvati in N ecuatiile:

a)      X + 4957 = 8734; x = 8734 – 4957; x = 3777;

b)      5043 + 2588 = x + 6230; 7631 = x + 6230; x = 1401;

c)      X – 1583 = 124; x= 124 + 1583; x = 1707;

d)      347 – x = 289; - x = - 58; x = 58;

e)      ( x – 2 ) * 3 = 12;

3x – 6 = 12 ; 3x = 12 + 6; 3x = 18; x = 18 : 3; x = 6;

f)       ( x – 2 ) * 5 = 0;                                            

5x – 10 = 0; 5x = 10; x = 10 : 5; x = 2;

g)      ( x – 1 )( x – 3 ) = 0;  ; x  { 1; 3}

h)      ( x – 1 ) * x = 0; ; x ( x – 1 ) = 0; ; x

i)        ( x – 3 ) : 3 = 7; ( x – 3 ) = 21; x = 24;

j)        ( 2x – 1 ) * 4 = 60; 8x – 4 = 60; 8x = 64; x = 64 : 8; x = 8;

k)      1000 : ( x – 5 ) = 200; 1000x : 500 = 200; 1000x = 1000; x = 1000 : 1000; x = 1;