Question

ajutati maaa ex 14.....​

Answer 1

Explicație pas cu pas:

a)

$\frac{ ^{3)} 2x + 5}{2} < \frac{^{2)}2x + 7}{3} \\ 3(2x + 5) < 2(2x + 7) \\ 6x + 15 < 4x + 14 \\ 6x - 4x < 14 - 15 \\ 2x < - 1 \implies x < - \frac{1}{2}$

b)

$\frac{ ^{2)}- x + 1}{3} > \frac{^{3)}7x + 8}{2} + ^{6)}1 \\ 2( - x + 1) > 3(7x + 8) + 6 \\ - 2x + 2 > 21x + 24 + 6 \\ - 2x - 21x > 30 - 2 \\ - 23x > 28 \implies x < - \frac{28}{23}$

c)

$\frac{^{3)}2x + 5}{2} < \frac{^{2)}5x}{3} + ^{6)}1 \\ 3(2x + 5) < 2 \times 5x + 6 \\ 6x + 15 < 10x + 6 \\ 6x - 10x < 6 - 15 \\ - 4x < - 9 \implies x > \frac{9}{4}$

d)

$\frac{^{2)}5x - 3}{2} < \frac{6x + 9}{4} + ^{4)}3 \\ 2(5x - 3) < 6x + 9 + 12 \\ 10x - 6 < 6x + 21 \\ 10x - 6x < 21 + 6 \\ 4x < 27 \implies x < \frac{27}{4}$