Question 465561
It's called "absolute value".
It means that whatever is inside
the bars, you ignore the minus if it
has a minus sign. Therefore:
{{{ abs(-10) = 10 }}}
{{{ abs(10) = 10 }}}
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You have:
{{{ abs(x-4) > 3 }}}
Try {{{ x = 4 }}}, then
{{{ abs(4-4) > 3 }}}
{{{ 0 > 3 }}} not true
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If {{{ 0 < x < 1 }}},
{{{ abs( .9 - 4 ) > 3 }}}
{{{ abs(-3.1) > 3 }}}
{{{ 3.1 > 3 }}} true
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Try {{{ x = 7 }}}
{{{ abs(7 - 4) > 3 }}}
{{{ 3 > 3 }}} also not true
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But if {{{ x > 7 }}},
{{{ abs(7.1 - 4) > 3 }}}
{{{ 3.1 > 3 }}} true
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If {{{ x <= 0 }}}, then
{{{ abs(-.1 - 4) > 3 }}}
{{{ 4.1 > 3 }}} true
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What it boils down to is,
there are 2 ranges for {{{x}}}
that make the inequality true:
{{{ x < 1 }}}
and
{{{ x > 7 }}} 
Anything between and including 
{{{1}}} and {{{7}}} fails
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Hope this helps