SOLVING

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SOLVING INEQUALITITES BY USING MULTIPLICATION
AND DIVISION
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MULTIPLICATION AND DIVISION PROPERTIES FOR
INEQUALITIES
For all numbers, a,b,and c, the following are
true. 1. If c is positive altb, then acltbc adn
a/cltb/c, and is c is positive and agtb, then
acgtbc and a/cgtb/c.
2. If c is negative and altb, then acltbc adn
a/cgtb/c, and if c is negative and agtb, then
acltbc and a/cltb/c.
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Example 1
e/1.5 gt 7
Multiply both sides by 1.5
1.5 (e/1.5) gt (7) 1.5
Since 1.5 is positive the inequality stays the
same.
e gt10.5
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Example 2
x/12 gt 3/2
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Example solve -3wgt27
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Angelica Moreno is a sales representative for an
appliance distributor. She needs at least 5000
in weekly sales for a particular TV model to
quality for a sales competition to win a trip to
the Bahamas. If the TVs sell for 250 each, how
many TVs will Ms. Moreno have to sell to qualify?
At least means she needs 5000 but would like
more, use gt Define t to represent the number of
t.v.s.
Divide both sides by 250 the inequality stays the
same, because 250 is positive
250t gt 5000
7
Triangle XYZ is not an acute triangle. The
greatest angle in the triangle has a measure of
(6d). What are the possible values of d?
6d
Since acute means less than 90. 6d must be gt 90.
6d gt 90 divide both sides by 6. Inequality
stays the same since 6 is positive