Question

calculati inegalitate. 2(x-1/3)+2-1/6>3x-2/2


numarul : 1.245. 1.246. 1.249. PLEASE!

Answer 1

$1.245 \\ a)2(x-\frac{1}{3})+\frac{2-x}{6}\ \textgreater \ \frac{3x-2}{2} \\\\ 2x-\frac{2}{3}+\frac{2-x}{6}\ \textgreater \ \frac{3x-2}{2} \\\\ \hbox{Se aduce la acelasi numitor-6} \\\\\\ 12x-4+2-x\ \textgreater \ 9x-6 \\\\ 11x-2\ \textgreater \ 9x-6 \\\\ 2x\ \textgreater \ -4 \\\\ x\ \textgreater \ -2 \to x\in [-2;+\infty)$



$b)\frac{x+4}{5}- \frac{3x-1}{2} \leq 2(x-1) \\\\ \hbox{Se aduce la acelasi numitor-10} \\\\\\ 2x+8-15x+5 \leq 20x-20 \\\\ -13x+13 \leq 20x-20 \\\\ -33x \leq -33 \ \ \ |:(-1) \\\\ x \geq 1 \to x\in [1;+\infty)$



$1.246 \\ a) \frac{3x+7}{8}-\frac{2x+1}{3} \geq \frac{1+x}{2} \\\\ \hbox{Se aduce la acelasi numitor-24} \\\\ 9x+21-16x-8 \geq 12+12x \\\\ -7x+13 \geq 12+12x \\\\ -19x \geq -1 \ \ |:(-1) \\\\ 19x \leq 1 \\\\ x \leq \frac{1}{19} \to x\in (-\infty;\frac{1}{19}]$



$b) \frac{4-5x}{3} \ \textless \ \frac{7x+1}{12}-2x \\\\ \hbox{Aducem la acelasi numitor-12} \\\\ 16-20x\ \textless \ 7x+1-24x \\\\ 16-20x\ \textless \ -17x+1 \\\\ -3x\ \textless \ -15 \ \ \ |:(-3) \\\\ x\ \textgreater \ 5 \to x \in (5;+\infty)$



$1.249 \\ a)\frac{x+1}{4}-\frac{4x+1}{5} \leq \frac{7-3x}{10} \\\\ \hbox{Aducem la acelasi numitor-20} \\\\ 5x+5-16x-4 \leq 14-6x \\\\ -11x+1 \leq 14-6x \\\\ -5x \leq 13 \ \ |(-1) \\\\ 5x \geq -13 \\\\ x \geq -\frac{13}{5} \to x\in [-\frac{13}{5};+\infty)$



$b)\frac{5-2x}{9} \geq \frac{x+2}{15}-\frac{7x-1}{5} \\\\ \hbox{Se aduce la acelasi numitor-45} \\\\ 25-10x \geq 3x+6-63x+9 \\\\ 25-10x \geq -60x+15 \\\\ 50x \geq -10 \\\\ 5x \geq -1 \\\\ x \geq -\frac{1}{5} \to x\in [-\frac{1}{5};\infty)$