Question 1009124
In the future, don't put your name ( or any other
personal information ) on the internet when you
don't have to. In other words, give away as little
personal data as you can.
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{{{ 2 - x >= 11 - 7 }}}
First, do the subtraction on the right side
{{{ 2 - x >= 4 }}}
Now you can subtract {{{ 2 }}} from both sides
{{{ -x >= 2 }}}
Now it looks like you can multiply both sides
by {{{ -1 }}} and you get {{{ x >= -2 }}}, but
you can't do this! 
Suppose I choose {{{ x = 10 }}}. In the 2nd 
equation, {{{ 10 >= -2 }}} TRUE, but in the 1st
equation: {{{ -10 >= 2 }}} NOT TRUE
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What you do is reverse the inequality sign
whenever you switch signs like this:
{{{ -x >= 2 }}}
{{{ x <= -2 }}}
Now you are OK. I'll say {{{ x = -10 }}}
2nd equation:
{{{ -10 <= -2 }}} OK
1st equation:
{{{ -(-10) >= 2 }}}
{{{ 10 >= 2 }}} OK
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So you have {{{ x <= -2 }}}
This is a vertical line intersecting the x-axis 
at ( -2, 0 )
The solution is the entire region to the 
left of this vertical line