Explicație pas cu pas:
a)
[tex] \frac{x + 4}{5} - \frac{x + 2}{3} = \frac{2x}{15} - \frac{x + 1}{3} \\ 3(x + 4) - 5(x + 2) = 2x - 5(x + 1) \\ 3x + 12 - 5x - 10 = 2x - 5x - 5 \\ - 2x + 2 = - 3x - 5 \\ - 2x + 3x = - 5 - 2 \\ - x = - 7 \\ x = 7[/tex]
b)
[tex] \frac{x}{2} - \frac{x + 7}{10} = \frac{x - 1}{4} - \frac{1}{5} \times (x + 1) + \frac{11}{20} \\ 10x - 2(x + 7) = 5(x - 1) - 4(x + 1) + 11 \\ 10x - 2x - 14 = 5x - 5 - 4x - 4 + 11 \\ 8x - 14 = x + 2 \\ 8x - x = 2 + 14 \\ 7x = 16 \\ x = \frac{16}{7} [/tex]
c)
[tex] \frac{3x - 2}{5} - \frac{1}{2} \times (x - 7) = \frac{15}{6} - \frac{1}{5} \times (2x - 9) \\ 6(3x - 2) - 15(x - 7) = 5 \times 15 - 6(2x - 9) \\ 18x - 12 - 15x + 105 = 75 - 12x + 54 \\ 3x + 93 = - 12x + 129 \\ 3x + 12x = 129 - 93 \\ 15x = 36 \\ x = \frac{36}{15} = > x = \frac{12}{5} [/tex]
d)
[tex] \frac{4x - 3}{7} - \frac{3 - x}{6} = \frac{2x + 1}{14} + \frac{13}{42} \\ 6(4x - 3) - 7(3 - x) = 3(2x + 1) + 13 \\ 24x - 18 - 21 + 7x = 6x + 3 + 13 \\ 31x - 39 = 6x + 16 \\ 31x - 6x = 16 + 39 \\ 25x = 55 \\ x = \frac{55}{25} = > x = \frac{11}{5} [/tex]
