Question

Resolva as inequações, sendo U = Q

Answer 1

a)

$\frac{1}{2} (x + 2) - \frac{1}{3}(x - 4) > \frac{1}{4}(x - 1) \\ \frac{6(x + 2) - 4(x - 4) > 3(x - 1) }{12} \\ 6(x + 2) - 4(x - 4) > 3(x - 1)$

$6x + 12 - 4x + 16 > 3x - 3 \\ 6x - 4x - 3x > - 3 - 12 - 16 \\ - x > - 31 \times ( - 1) \\ x < 31$

b)

$\frac{x - 1}{2}+x<\frac{x - 2}{4} + \frac{x - 3}{5} \\ \frac{10(x - 1) + 20x < 5(x - 2) + 4(x - 3)}{20}$

$10x - 10 + 20x < 5x - 10 + 4x - 12 \\ 10x + 20x - 5x - 4x < 10 - 10 - 12 \\ 21x < - 12 \\ x < - \frac{12 \div 3}{21 \div 3}$

$x < - \frac{4}{7}$

c)

$3(x + 1) < 4(x + 2) \\ 3x + 3 < 4x + 8 \\ 3x - 4x < 8 - 3 \\ - x < 5 \times ( - 1) \\ x > - 5$

d)

$4(x - 1) + 6(x - 2) \leqslant 0 \\ 4x - 4 + 6x - 12 \leqslant 0 \\ 4x + 6x \leqslant 12 + 4 \\ 10x \leqslant 16$

$x \leqslant \frac{16 \div 2}{10 \div 2} \\ x \leqslant \frac{8}{5}$