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-4 < 3x - 1 < 5
Add +1 to all three sides
-4 < 3x - 1 < 5
+1 +1 +1
-3 < 3x < 6
-3 < 3x < 6
Divide all three sides by the coefficient of x which is 3:
-1 < x < 2
Draw this number line and put an open circle "o" at -1 since
the inequality < on that side is not underlined and a closed
circle "@" at 2 because the inequality symbol < on that side
is underlined:
---------o-----------@--------
-3 -2 -1 0 1 2 3 4
Shade the line between them:
---------o===========@--------
-3 -2 -1 0 1 2 3 4
That's it. An abbreviation for that is called "interval notation".
It is
(-1, 2]
The ( indicates an open circle on the left end of the interval and
the ] indicates a closed circle on the right end of the interval.
Edwin
