Readings for Session 7 – (Continued)
Compound Inequalities
Each week for the past year,
Raul’s Balloon Emporium’s weekly profit was as high as $9,540
and as low as $4,274.
We often express problems of this
type algebraically with a compound inequality. We may express
the problem as
4,274
≤
P ≤
9,540
where P represents a weekly
profit. The expression may be interpreted as “all the values
P for which
P is greater than or equal to 4,274 and
P is less than or equal to 9,540.
Based on what we did earlier in
this session, what would the interpretation be in terms of the
language of sets? Or, how does this problem relate to sets?
Example: 4 < x ≤ 10 means
“all the values of x
for which 4 is less than x, and x
is less than or equal to 10.”
The inequality signs in a compound inequality should both point
the same direction.
Compound inequalities are often written in set-builder notation.
Notice how the “universal set” is specified in these
examples.
Example:
{x : 4 <
x
≤ 10,
x
∈ N } = {5,
6, 7, 8, 9, 10}
Example: {x
: 0
≤
x
< 5,
x
∈
W
} = {0, 1, 2, 3, 4}
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