Question 145484
{{{-2(3+x)<4x+4<8x}}}
<pre>
When given {{{A < B < C}}} 

Solve  {{{A < B}}}

Solve  {{{A < C}}}

Solve  {{{B < C}}}

Take the intersection of all three solution sets

{{{-6-2x < 4x + 4 < 8x }}}

First solve:

{{{-6-2x < 4x + 4}}}

  {{{-6x < 10}}}
    {{{x > -5/3}}}    

Now solve

{{{4x + 4 < 8x}}}
   {{{-4x < -4}}}
     {{{x > 1}}}

Now solve

 {{{-6-2x < 8x}}}

  {{{-10x < 6}}}
     
     {{{x > -3/5}}}  

The intersection of those three sets is {{{x > 1}}}, for
if we choose {{{x > 1}}} then the other two {{{x > -5/3}}}
and {{{x > -3/5}}} are automatically satisfied.

Answer:  x > 1 or in interval notation  (1,{{{infinity}}})