Question

What is the solution of x^2+x-6/x-7<0 PLEASE HELP ME :( (it’s not the 2nd one i already tried it)

Answer 1

Answer:

the first one  $\:x\le \:-3\quad \mathrm{or}\quad \:2\le \:x$

Step-by-step explanation:

Factor $x^2+x-6$ :

Break the expression into groups

$\left(x^2-2x\right)+\left(3x-6\right)$

$\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2-2x\mathrm{:\quad}$

$x\left(x-2\right)$

$\mathrm{Factor\:out\:}3\mathrm{\:from\:}3x-6\mathrm{:\quad}$

$3\left(x-2\right)$

$x\left(x-2\right)+3\left(x-2\right)$

$\mathrm{Factor\:out\:common\:term\:}x-2$

$\left(x-2\right)\left(x+3\right)$

$\frac{\left(x-2\right)\left(x+3\right)}{x-7}$

$\frac{\left(x-2\right)\left(x+3\right)}{x-7}\le \:0$

$\mathrm{Find\:the\:signs\:of\:the\:factors\:of\:}\frac{\left(x-2\right)\left(x+3\right)}{x-7}$

$\mathrm{Identify\:the\:intervals\:that\:satisfy\:the\:required\:condition:}\:\le \:\:0$

$x$

Merge Overlapping Intervals

$x\le \:-3\quad \mathrm{or}\quad \:2\le \:x$