Explicație pas cu pas:
[tex]a) \frac{3x - 5}{2} - \frac{5x + 1}{4} = \frac{2x + 6}{8} - \frac{3x - 12}{6} - 1 \\ \\ \frac{4(3x - 5) + 2( - (5x + 1))}{2 \times 4} = \frac{2x + 2 \times 3}{8} - \frac{3x - {2}^{2} \times 3 }{6} - 1 \\ \\ \frac{4(3x - 5) - 2(5x + 1)}{2 \times 4} = \frac{2( \frac{2x}{2} + \frac{2 \times 3}{2}) }{8} - \frac{3( \frac{3x}{3} - \frac{ {2}^{2} \times 3 }{3}) }{6} - 1 \\ \\ \frac{(4 \times 3x - 4 \times 5) - (2 \times 5x + 2)}{2 \times 4} = \frac{2(x + 3)}{8} - \frac{3(x - {(2}^{2})) }{6} - 1 \\ \\ \frac{(12x - 20) - (10x + 2)}{2 \times 4} = \frac{x + 3}{4} - \frac{3(x - 4)}{6} - 1 \\ \\ \frac{12x - 20 - 10x - 2}{2 \times 4} = \frac{x + 3}{4} - \frac{x - 4}{2} - 1 \\ \\ \frac{12x - 10x - 20 - 2}{2 \times 4} = \frac{2(x + 3) + 4( - (x - 4)) - (4 \times 2)}{4 \times 2} \\ \\ \frac{2x - 22}{2 \times 4} = \frac{2(x + 3) - 4(x - 4) - 8}{4 \times 2} \\ \\ \frac{2x - 2 \times 11}{2 \times 4} = \frac{(2x + 2 \times 3) - (4x - 4 \times 4) - 8}{4 \times 2} \\ \\ \frac{2( \frac{2x}{2} - \frac{2 \times 11}{2}) }{2 \times 4} = \frac{(2x + 6) - (4x - 16) - 8}{4 \times 2} \\ \\ \frac{2(x - 11)}{2 \times 4} = \frac{2x + 6 - 4x + 16 - 8}{4 \times 2} \\ \\ \frac{x - 11}{4} = \frac{2x - 4x + 6 + 16 - 8}{4 \times 2} \\ \\ \frac{x - 11}{4} = \frac{ - 2x + 14}{4 \times 2} \\ \\ \frac{x - 11}{4} = \frac{ - 2x + 2 \times 7}{4 \times 2} \\ \\ \frac{x - 11}{4} = \frac{2( - \frac{2x}{2} + \frac{2 \times 7}{2}) }{4 \times 2} \\ \\ \frac{x - 11}{4} = \frac{2( - x + 7)}{4 \times 2} \\ \\ \frac{x - 11}{4} = \frac{ - x + 7}{4} \\ \\ \frac{x - 11}{ {2}^{2} } = \frac{ - x + 7}{ {2}^{2} } \\ \\ x - 11 = - x + 7 \\ \\ (x - 11) + (11 + x) = ( - x + 7) + (11 + x) \\ \\ x - 11 + 11 + x = - x + 7 + 11 + x \\ \\ x + x - 11 + 11 = - x + x + 7 + 11 \\ \\ 2x = 18 \\ \\ \frac{2x}{2} = \frac{18}{2} \\ \\ x = 9 [/tex]
