You can
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4x-6 < 2x < 5x+3
Break into two inequalities, and solve each
for x:
4x-6 < 2x AND 2x < 5x+3 MUST BOTH BE TRUE
2x < 6 AND -3x < 3 MUST BOTH BE TRUE
x < 3 AND x > -1 MUST BOTH BE TRUE
x < 3 AND -1 < x MUST BOTH BE TRUE
-1 < x AND x < 3 MUST BOTH BE TRUE
THOSE INEQUALITIES CAN NOW BE COMBINED
WITH x IN THE MIDDLE AS
-1 < x < 3
which represents this interval on the number line:
-------o===========o------
-3 -2 -1 0 1 2 3 4 5
In interval notation that's (-1, 3)
Edwin
