Question

rezolvati in Z inecuatiile:
a)2(x+3)-x<4-5x
b)-x>4(3x-2)-5x+7
c)3(x-2)-5(x+4)<-8+x
d)3-2x-4(x-5)≥-1+3x
e)-6+5(x+2)≤3x-5(2x-1)
f)2x-2(3x-7)+1>3(5x-1)
g)3(6-8x)-(2x+3)≤3x-4

Answer 1

$\displaystyle a).2(x+3)-x\ \textless \ 4-5x \\ 2x+6-x\ \textless \ 4-5x \\ 2x-x+5x\ \textless \ 4-6 \\ 6x\ \textless \ -2 \\ x\ \textless \ - \frac{2}{6} \\ x\ \textless \ - \frac{1}{3} \\ b).-x\ \textgreater \ 4(3x-2)-5x+7 \\ -x\ \textgreater \ 12x-8-5x+7 \\ -x-12x+5x\ \textgreater \ -8+7 \\ -8x\ \textgreater \ -1 \\ x\ \textless \ \frac{1}{8}$
$\displaystyle c).3(x-2)-5(x+4)\ \textless \ -8+x \\ 3x-6-5x-20\ \textless \ -8+x \\ 3x-5x-x\ \textless \ -8+6+20 \\ -3x\ \textless \ 18 \\ x\ \textless \ - \frac{18}{3} \\ x\ \textgreater \ -6 \\ d).3-2x-4(x-5) \geq -1+3x \\ 3-2x-4x+20 \geq -1+3x \\ -2x-4x-3x \geq -1-3-20 \\ -9x \geq -24 \\ x \leq \frac{24}{9} \\ x \leq \frac{8}{3}$
$\displaystyle e).-6+5(x+2) \leq 3x-5(2x-1) \\ -6+5x+10 \leq 3x-10x+5 \\ 5x-3x+10x \leq 5+6-10 \\ 12x \leq 1 \\ x \leq \frac{1}{12} \\ f).2x-2(3x-7)+1\ \textgreater \ 3(5x-1) \\ 2x-6x+14+1\ \textgreater \ 15x-3 \\ 2x-6x-15x\ \textgreater \ -3-14-1 \\ -19\ \textgreater \ -18 \\ x\ \textless \ \frac{18}{19}$
$\displaystyle g).3(6-8x)-(2x+3) \leq 3x-4 \\ 18-24x-2x-3 \leq 3x-4 \\ -24x-2x-3x \leq -4-18+3 \\ -29x \leq -19 \\ x \geq \frac{19}{29}$