Question

Exercitiul A1:Sa se rezolve sistemele de inecuatii:

Answer 1

Răspuns:

a) x € (-○○; -2) U (-1; -3/4}

Explicație pas cu pas:

$\frac{x + 2}{3} + \frac{1}{2} - x - \frac{5}{3} > 0 \\ \frac{x + 2}{x + 1} - \frac{x}{2(x + 1)} > 0 \\ \\ \frac{2(x + 2) + 3 \times 1 - 6 \times x - 2 \times 5}{6} > 0 \\ \frac{2(x + 2) - x}{2(x + 1)} > 0 \\ \\ \frac{2x + 4 + 3 - 6x - 10}{6} > 0 \\ \frac{2x + 2 - x}{2(x + 1)} > 0\\ \\ \frac{ - 4x - 3}{6} > 0 \\ \frac{x + 2}{2(x + 1)} > 0 \\ \\ - 4x - 3 > 0 = > 4x < - 3 = > x < - \frac{3}{4} \\ \frac{x + 2}{2(x + 1)} > 0 = > x < - 2 \: sau \: x > - 1 \\ \\ x < - 2 \: sau \: - 1 < x < - \frac{3}{4}$