Question

For which of the following compound inequalities is there no solution? Select one: a. 8m+5>=5 and -4m+6<=-10 b. 6m<=-36 and m+24>20 c. -2m< 6 and 3m>24 d. m+9<8 and -2m>=10

Answer 1

$a.\\8m+5\geq5\ \ \ |-5\\8m\geq0\ \ \ |:8\\m\geq0\to m\in\left<0;\ \infty\right)\\\\-4m+6\leq-10\ \ \ |-6\\-4m\leq-16\ \ \ |:(-4)\\m\geq4\to m\in\left<4;\ \infty\right)\\\\solution:\ m\in\left<0;\ \infty\right)\ \cap\ \left<4;\ \infty\right)\to m\in\left<4;\ \infty\right)$

$b.\\6m\leq-36\ \ \ |:6\\m\leq-6\to m\in\left(-\infty;\ -6\right>\\\\m+24 > 20\ \ \ |-24\\m > -4\to m\in(-4;\ \infty)\\\\solution:\ m\in\left(-\infty;\ -6\right>\ \cap\ (-4;\ \infty)\to m\in\O\to NO\ SOLUTION$

$c.\\-2m < 6\ \ \ |:(-2)\\m > -3\to m\in(-3;\ \infty)\\\\3m > 24\ \ \ |:3\\m > 8\to m\in(8;\ \infty)\\\\solution:\ m\in(-3;\ \infty)\ \cap\ (8;\ \infty)\to m\in(8;\ \infty)$

$d.\\m+9 < 8\ \ \ |-9\\m < -1\to m\in(-\infty;\ -1)\\\\-2m \geq10\ \ \ |:(-2)\\m\leq-5\to m\in\left(-\infty;-5\right>\\\\solution:\ m\in(-\infty;\ -1)\ \cap\ \left(-\infty;-5\right>\to m\in\left(-\infty;-5\right>$