Sometimes these shortcuts are great and other times
they seem to be "too tricky" to make sense when the
same type problem needs attention later.
One particular case is graphing an Open Sentence
that is an INEQUALITY.
For example:
Graph the Solution Set for "5 < x"
During my teaching days I found that some of
my students were taught to always have the
"X" on the left so that the > or < will point in the
direction of the shaded solution. This requires
the student to sometimes "SWITCH" the direction
that the inequality sign points. (This switching only
occurs when "X" is on the RIGHT SIDE!)
so "5 < x" becomes "x > 5"
the graph is ...
The idea of 1) moving the x to the LEFT,
2) switching the direction of "<" to ">"
and then 3) pointing the arrow of the graph in the
direction of ">" does produce a correct graph.
My suggestion is to encourage the students
to read the inequality starting with "X".
"5 < x"
would be read "X is GREATER than 5."
Since we are graphing "X's", this method
of translation will lead to the correct
direction of the ARROW in the graph.
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