Question 159777
x-6/x+2 < -1 how do you solve and graph this inequality?
:
Assume you mean (brackets are wonderful devices)
{{{((x-6))/((x+2))}}} < -1 
:
Multiply both sides by (x+2), results
x - 6 < -1(x+2)
:
x - 6 < -x - 2
:
x + x < -2 + 6
:
2x < 4
x < {{{4/2}}}
x < 2
:
:
Check it with a value slightly less than 2, x = 1.8
{{{((1.8-6))/((1.8+2))}}} < -1 
{{{(-4.2)/3.8}}} < -1
-1.1 < -1; is true
:
Graphing this:
 x | y
---------
-10|+3
-6 |+4
-3 |+10
-2 | no value here, division by 0 in the original equation
-1 |-6
 0 |-2
+2 | 0
+3 |.4
+6 | 1
+8 |+1.2

{{{ graph( 300, 200, -10, 10, -10, 10, ((x-6)/(x+2))+1 ) }}}
Ignore the area between -1 and -3
The area for this equation is below the line