Question 1003018
Starting simple, suppose you have 2 quantities,
{{{ a }}} and {{{ b }}}, then
(1) {{{ a > b }}} means:
[ quantity {{{a}}} ] is GREATER than [ quantity {{{b}}} ]
(2) {{{ a < b }}} means:
[ quantity {{{a}}} ] is LESS than [ quantity {{{b}}} ]
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Now if you add on the equals sign, you have:
(3) {{{ a >= b }}} means:
[ quantity {{{a}}} ] is GREATER than OR EQUAL to  [ quantity {{{b}}} ]
(4) {{{ a <= b }}} means:
[ quantity {{{a}}} ] is LESS than OR EQUAL to [ quantity {{{b}}} ]
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You have to keep in mind that {{{ -3 > -7 }}} is a true statement
The quantities can be any number on the number line
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A potential sticky point is the following:
If you divide both sides by a negative number, then the
inequality sign has to be reversed.
Example:
{{{ 10 >5 }}}
Divide both sides by {{{ -5 }}}
{{{ 10/(-5) > 5/(-5) }}}
{{{ -2 > -1 }}} oh-oh, this is NOT TRUE, but if
I reverse the inequality sign,
{{{ -2 < -1 }}} OK now
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As for your example, it reads:
The function {{{ g(x) }}} is LESS THAN OR EQUAL to {{{ 2x }}}
and {{{ g(x) }}} is also GREATER THAN OR EQUAL to {{{ -2x }}}
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You don't have to put this on one line
You can break it up into 2 statements:
{{{ -2x <= g(x) }}}
{{{ g(x) <= 2x }}}
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Also note that you can spin the inequality around and
it's still true:
{{{ g(x) >= -2x }}} is perfectly valid also
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You can treat inequalities just like equations by adding,
subtracting, multiplying, dividing both sides by the
same quantity EXCEPT the special case of dividing by
a negative number just noted.
Hope this helps