&KDSWHU3-5
Update your skills. See page 412 XII.Solve Inequalities Using Multiplication
Objective To solve one-step inequalities by applying the Multiplication Property
of Inequality • To graph the solution set of an inequalityFive friends evenly divided the cost of a trip to Yosemite
National Park. Each friend paid a whole dollar amount
that was at most $13. What was the total cost of the trip?
To find the total cost of the trip, write and solve an inequality.
Let c the total cost of the trip.total cost divided by number of friends is at most cost per friendc 5 $13
Solve inequalities involving division the same way that you
solve division equations.Solve:
13(5) 13(5)13 • 5 Simplify.c
65
So the solution set is the whole numbers less than 65.Check: According to the solution set, 65 is a solution and 70 is not.13 Substitute 65 for c. 13 Substitute 70 for c.13
13 Tr u e 14
13 False
The total cost of the trip was whole dollar amounts of $65 or less.When an inequality is multiplied by a negative number,
the symbol must be reversed to form a true statement.Solve: 12(3) 12(3)p 36 Simplify.
So the solution set is all numbers greater than 36.
Check: According to the solution set,
33 is a solution and 36 is not.12 Substitute 33 for p. 12 Substitute 36 for p.11 12 Tr u e 12 12 False 36
3 33
3p
3
p
370
565
5
??c
55
511c? ?Multiply both sides by 3
to isolate pand reverse the
inequality symbol.c
5 Multiply both sides
by 5 to isolate c.Key Concept
Multiplication Property of Inequality
(multiply by a positive number)
When you multiply both sides of an
inequality by the same positive
number, you get a true statement.
If aband cis positive, then acbc.
A similar statement can be written for
ab, a b, and a b.Key Concept
Multiplication Property of Inequality
(multiply by a negative number)
When you multiply both sides of an
inequality by the same negativenumber
andyou reverse the inequality symbol,
you get a true statement.
If aband cis negative, then acbc.
A similar statement can be written for
ab, a b, and a b.Think5 cmeans c^5