Question

Resolva as inequações, sendo U = IR conjunto universo

c) x-2 / 4 + 1/2 > x - 2x - 1 /3

d) 1+ 3x + 1/2 < 2x / 3 + x+1 / 4

5x - 1 / 6 - x/2 < 1

Answer 1

Explicação passo-a-passo:

$a) \frac{x - 2}{4} + \frac{1}{2} > x - 2x - \frac{1}{3} \: \: \: mmc = 12$

$x - 2 + 6 > 12x - 24x - 4$

$x - 12x + 24x > - 4 - 6 + 2$

$13x > - 8 \\ x > \frac{ - 8}{13}$

$b)1 + 3x + \frac{1}{2} < \frac{2x}{3} + \frac{x + 1}{4} \: \: mmc = 12$

$12 + 36x + 6 < 8x + 3.(x + 1)$

$12 + 36x + < 8x + 3x + 3$

$36x - 8x - 3x = 3 - 12 \\ 25x = - 9 \\ x = \frac{ - 9}{25}$

$c)5x - \frac{1}{6} - \frac{x}{2} < 1 \: \: \: mmc = 6$

$30x - 1 - 3x < 6$

$27x < 6 + 1 \\ 27x < 7 \\ x < \frac{7}{27}$