Solving Inequalities
An equation states that the values on either side of the
= sign
are of the same value. An inequality states that one side of the
equation is greater than the other:
a < b states
that
a is less than
b,
while
a > b states
that
a is greater than b.
means
that
a is less than or equal to
b, while
means
that
a is greater than or equal to
b.
Solving an inequality is basically the same as solving
a normal equation: all the rules of simplification still apply,
as does the rule stipulating that whatever you do to one side of
the equation you must also do to the other side. The one rule that
does differ for inequalities comes when you multiply both sides
by a negative. If you do so, you must flip the greater than or less
than sign: if x > y, then –x <
–y.
Inequalities often appear in QC questions.
The fastest way to answer this question is to substitute
7/2 into
the inequality
2 < 2y – 3 < 9 to
see if it is a possible value for
y.
If you did this, you’d see that
2(7
/2) – 3 = 4,
making
7/2 a possible
value for
y. Also, because when
7/2 is
plugged into the expression it gives you the value of
4,
which is the highest possible allowed value of the expression as
stated by
you know that
y can
never be bigger than
7/
2. And since the expression
in column A is
y – 1, you know that
Column B must be bigger than Column A.
