Question

rezolvati in Z inecuatiile:
a)$\frac{3x-2}{4} -1$≤$\frac{2}{3} x + \frac{2x-5}{6}$
b)$\frac{5x-1}{2} - \frac{4x-3}{5} \ \textgreater \ 2x - \frac{3x+1}{10}$
c)$\frac{3-x}{8} + \frac{3}{4} -x$≤$1- \frac{2x+1}{6}$
d)x - $\frac{3x-2}{5} \ \textless \ 2(3-x)+ \frac{x}{6} + \frac{11}{10}$

Answer 1

$\displaystyle a). \frac{3x-2}{4} -1 \leq \frac{2}{3} x+ \frac{2x-5}{6} \\ 3(3x-2)-12 \leq 8x+2(2x-5) \\ 9x-6-12 \leq 8x+4x-10 \\ 9x-8x-4x \leq -10+6+12 \\ -3x \leq 8 \\ x \geq - \frac{8}{3} \\ b). \frac{5x-1}{2} - \frac{4x-3}{5} \ \textgreater \ 2x- \frac{3x+1}{10} \\ 5(5x-1)-2(4x-3)\ \textgreater \ 20x-3x+1 \\ 25x-5-8x+6\ \textgreater \ 20x-3x-1 \\ 25x-8x-20x+3x\ \textgreater \ -1+5-6 \\ 0\ \textgreater \ -2$
$\displaystyle c). \frac{3-x}{8} + \frac{3}{4} -x \leq 1- \frac{2x+1}{6} \\ 3(3-x)+18-24x \leq 24-4(2x+1) \\ 9-3x+18-24x \leq 24-8x-4 \\ -3x-24x+8x \leq 24-4-9-18 \\ -19x \leq -7 \\ x \geq \frac{7}{19} \\ d).x- \frac{3x-2}{5} \ \textless \ 2(3-x)+ \frac{x}{6} + \frac{11}{10} \\ 30x-6(3x-2)\ \textless \ 6-2x+5x+33 \\ 30x-18x+12\ \textless \ 6-2x+5x+33 \\ 30x-18x+2x-5x\ \textless \ 6+33-12 \\ 9x\ \textless \ 27 \\ x\ \textless \ \frac{27}{9} \\ x\ \textless \ 3$