Question

Resolva o sistema de inequação:
x/3 - x-2/5 < 2
3(x-6)/4 > 0?

Answer 1

$\frac{x}{3} - \frac{(x-2)}{5} \ \textless \ 2\\ \frac{3(x-6)}{4} \ \textgreater \ 0\\\\\\ \frac{x}{3} - \frac{(x-2)}{5} \ \textless \ 2\to mmc=15\\\\ 5x-(3x-6)\ \textless \ 30\to \\\\5x-3x+6\ \textless \ 30\to \\\\5x-3x\ \textless \ 30-6\to \\\\ 2x\ \textless \ 24\to\\\\ x\ \textless \ \frac{24}{2} \to \\\\x\ \textless \ 12$



$\frac{3(x-6)}{4} \ \textgreater \ 0 \to mmc=4\to \\\\ 3(x-6)\ \textgreater \ 0\to \\\\3x-18\ \textgreater \ 0\to\\\\ 3x\ \textgreater \ 18\to\\\\ x\ \textgreater \ \frac{18}{3} \to\\\\ x\ \textgreater \ 6\\\\\\\\\\ S=\{xER| 6\ \textless \ x\ \textless \ 12\}$

Answer 2

x  - x - 2  < 2
3      5

mmc (3,5) = 15

5x - 3(x - 2) < 15.2
     15               15

5x - 3x + 6 < 30
2x + 6 < 30
2x < 30 - 6
2x < 24
x < 24/2
x < 12

3(x - 6) > 0
    4

3x - 18 > 0.4
3x - 18 > 0
3x > 18
x > 18/3
x > 6

Se x > 6 e x < 12, então:

R.: {x∈ R / 6 < x < 12}