Question

Решите неравенства a)0.3(x-2)-0.8> -4.4 b)15-3x/12≥5 c)2x-1/3< 5 d)3> 6-x/4 e)2/7(x-4)> 3 f)7-2x/2≥3x-7/4

Answer 1

$1)\; \; 0,3(x-2)-0,8\ \textless \ -4,4\\\\0,3x-0,6-0,8\ \textless \ -4,4\\\\0,3x\ \textless \ -3\; ,\; \; \; \underline {x\ \textless \ -10}\\\\2)\; \; \frac{15-3x}{12} \geq 5\\\\15-3x \geq 60\; ,\; \; -3x\ \textgreater \ 45\; ,\; \; \; \underline {x\ \textless \ -15}\\\\ 3)\; \; \frac{2x-1}{3}\ \textless \ 5\\\\2x-1\ \textless \ 15\; ,\; \; 2x\ \textless \ 16\; ,\; \; \underline {x\ \textless \ 8} \\\\4)\; \; 3\ \textgreater \ \frac{6-x}{4} \\\\12\ \textgreater \ 6-x\; ,\; \; 6\ \textgreater \ -x\; ,\; \; \underline {x\ \textgreater \ -6}\\\\5)\; \; \frac{2}{7(x-4)} \ \textgreater \ 3\; ,\; \; \frac{2}{7(x-4)}-3\ \textgreater \ 0\\\\\frac{2-21(x-4)}{7(x-4)}\ \textgreater \ 0\; ,\; \frac {-21x+86}{7(x-4)}\ \textgreater \ 0\; ,\; \frac{-(21x-86)}{7(x-4)}\ \textgreater \ 0,$

$\frac{21(x-\frac{86}{21})}{7(x-4)}\ \textless \ 0\; ,\; \; +++(4)---(\frac{86}{21})+++\\\\\underline {x\in (4;4\frac{2}{21})}\\\\6)\; \; \frac{7-2x}{2} \geq \frac{3x-7}{4} \; |\cdot 4\\\\2(7-2x) \geq 3x-7\\\\14-4x \geq 3x-7\\\\21 \geq 7x\\\\\underline {x\leq 3}$