Question 160478
{{{(x-11)(x-8) > 0}}}
I got {{{8 < x > 11}}}
but the answer was {{{8 > x > 11}}}
<pre><font size = 4 color = "indigo"><b>
That's not correct.  Sometimes answers in books are wrong.
But your answer is wrong too.  "{{{8 < x > 11}}}" is NEVER written.
In an inequality with more than two sides or parts, all the
inequalities must be pointed the same way.  That is a rule
which must be followed.  

The correct answer is

{{{matrix(1,3,x<8, OR, x>11)}}}

And that is the only way to write it, unless you use
interval notation, which is

{{{matrix(1,11, "(",-infinity,  ",", 8, ")", U, "(", "11", ",", infinity, ")"  )}}} 

Graphed on a number line the solution is

<==============================o--------o======>
-2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 13   

Do you want to know how to solve it correctly?

Here is how:

{{{(x-11)(x-8) > 0}}}

The left side becomes 0 if {{{x=11}}} or if {{{x=8}}}.

Draw this number line:

<--------------------------------------------->
-2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 13  

Draw open circles at 11 and 8

<------------------------------o--------o----->
-2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 13 

Choose any value left of x=8, say x=0. Plug it in

{{{(x-11)(x-8) > 0}}}
{{{(0-11)(0-8) > 0}}}
{{{(-11)(-8) > 0}}}
{{{88>0}}}

That is true so shade the whole side left of 8

<==============================o--------o----->
-2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 13

Choose any value right of x=8 that is also left of 11,
say x=9. Plug it in

{{{(x-11)(x-8) > 0}}}
{{{(9-11)(9-8) > 0}}}
{{{(-2)(1) > 0}}}
{{{-2>0}}}

That is false so we DO NOT shade the part between
8 and 11. So we still have:

<==============================o--------o----->
-2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 13

Choose any value right of x=11, say x=12. Plug it in

{{{(x-11)(x-8) > 0}}}
{{{(12-11)(12-8) > 0}}}
{{{(1)(4) > 0}}}
{{{4>0}}}

That is true so shade the whole side right of 8

<==============================o--------o======>
-2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 13

So to describe where a number x is located on that
number line you say: 

"x is either less than 8 OR x is greater than 11"

{{{matrix(1,3,x<8, OR, x>11)}}}

or in interval notation:

{{{matrix(1,11, "(",-infinity,  ",", 8, ")", U, "(", "11", ",", infinity, ")"  )}}}

Edwin</pre>