Explicação passo-a-passo:

[tex]a) \frac{x - 2}{4} + \frac{1}{2} > x - 2x - \frac{1}{3} \: \: \: mmc = 12[/tex]

[tex]x - 2 + 6 > 12x - 24x - 4[/tex]

[tex]x - 12x + 24x > - 4 - 6 + 2[/tex]

[tex]13x > - 8 \\ x > \frac{ - 8}{13} [/tex]

[tex]b)1 + 3x + \frac{1}{2} < \frac{2x}{3} + \frac{x + 1}{4} \: \: mmc = 12[/tex]

[tex]12 + 36x + 6 < 8x + 3.(x + 1)[/tex]

[tex]12 + 36x + < 8x + 3x + 3[/tex]

[tex]36x - 8x - 3x = 3 - 12 \\ 25x = - 9 \\ x = \frac{ - 9}{25} [/tex]

[tex]c)5x - \frac{1}{6} - \frac{x}{2} < 1 \: \: \: mmc = 6[/tex]

[tex]30x - 1 - 3x < 6[/tex]

[tex]27x < 6 + 1 \\ 27x < 7 \\ x < \frac{7}{27} [/tex]