Question 138541
Given : {{{x + 11 < - 2}}}  or {{{x + 11 > 4}}}

The first thing you need to do is isolate x in each equation
{{{x + 11 < - 2}}}  subtract 11 from each side
{{{x  < - 13}}} 

Now do the same for the second equation
{{{x + 11 > 4}}}  again subtract 11
{{{x > -7}}}

So if we replace the values we just calculated in the original equation:
{{{x + 11 < - 2}}}  or {{{x + 11 > 4}}}
{{{x  < - 13}}} or {{{x > -7}}}

The solution set is any x that us less than -13 OR greater that -7. In the number line below, that is any x to the left of -13 (the red point) and any x to the right of -7 (the green point)
{{{number_line( 600, -15, 5, -13, -7 ) }}}