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

The answer would be A

Hope this helps!!!

Explanation:

Answer 2

the first one
`\:x\le \:-3\quad \mathrm{or}\quad \:2\le \:x<7`

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)`

`(\left(x-2\right)\left(x+3\right))/(x-7)\\`

`(\left(x-2\right)\left(x+3\right))/(x-7)\le \:0`

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

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

`x<-3\quad \mathrm{or}\quad \:x=-3\quad \mathrm{or}\quad \:x=2\quad \mathrm{or}\quad \:2<x<7`

Merge Overlapping Intervals

`x\le \:-3\quad \mathrm{or}\quad \:2\le \:x<7`