Question

Rezolvati, in multimea numerelor reale, ecuatia 2x+3/9-2/3*(x+2)=2x-5/18+x/6

Answer 1

2x + 3/9 - 2x/3 - 4/3 = 2x - 5/18 + x/6
Numitor comun 18
36x + 6 - 12x - 24 = 36x - 5 + 3x
-12x - 18 = 3x - 5
-15x = 13
x = -13/15

Answer 2

$2x + \frac{3}{9} - \frac{2}{3} \times (x + 2) = 2x - \frac{5}{18} + \frac{x}{6} \\ \\ \frac{3}{9} - \frac{2}{3}(x + 2) = - \frac{5}{18} + \frac{x}{6} \\ \\ \frac{1}{3} - \frac{2(x + 2)}{3} = - \frac{5}{18} + \frac{x}{6} \\ \\ \frac{1 - 2(x + 2)}{3} = - \frac{5}{18} + \frac{x}{6} \\ \\ \frac{1 - 2(x + 2)}{3} = \frac{x}{6} - \frac{5}{18} \\ \\ 2( - 2x - 3) = x - \frac{5}{3} \\ \\ - 4x - 6 = x - \frac{5}{3} \\ \\ - 6 = x - \frac{5}{3} + 4x \\ \\ - 6 = 5x - \frac{5}{3} \\ \\ - 6 + \frac{5}{3} = 5x \\ \\ - \frac{13}{3} = 5x \\ \\ - \frac{ \frac{13}{3} }{5} = x \\ \\ - \frac{13}{3 \times 5} = x \\ \\ - \frac{13}{15} = x \\ \\ x = - \frac{13}{15}$