Transcript Chapter 7 Lesson 5 Solving Inequalities by Multiplying or Dividing

Chapter 7 Lesson 5
Solving Inequalities by
Multiplying or Dividing
pgs. 350 - 354
What you’ll learn:
Solve inequalities by multiplying or
dividing by positive & negative
numbers
Key Concept:
Multiplication & Division
Properties (pg. 350)
» Words: When you multiply or
divide each side of an
inequality by the same
POSITIVE number, the
inequality remains true.
» Symbols: For all numbers a, b,
and c, where c > 0
1. If a > b, then ac>bc and a > b
c c
2. If a < b, then ac<bc and a < b
c
c
Key Concept Continued:
» Examples:
2<6
4(2) < 4(6)
8 < 24
3 > -9
3 > -9
3
3
1 > -3
These properties are also true for a  b and a  b
Example 1: Multiply or Divide
by a Positive Number
» Solve 7y > 63 Check your solution
Write the inequality: 7y > 63
Divide each side by 7: 7y > 63
7
7
Simplify: y > 9
The solution is y > 9. You can check this
solution by substituting a number greater than
9 into the inequaltiy.
Check: Let’s check with 11
7(11) > 63
77 > 63 
Example 1: Another Look
» Solve 6  x
7
Check your solution
Write the inequality: 6  x
7
Multiply each side by 7: (7)6  x(7)
7
Simplify: 42  x which also means x  42
The solution is x  42 You can check this solution by
substituting 42 or a number less than 42 into the inequality.
Check using 35: 6  35
65
7
Example 2: Write an
inequality
Julia delivers pizza on weekends. Her
average tip is $1.50 for each pizza that
she delivers. How many pizzas must
she deliver to earn at least $20 in tips?
A. 10
B. 13
C. 14
D. 20
Solve: Let x represent the number of pizzas.
1.50 = average per pizza
 = times
x = number of pizzas
 = at least
20 = total amount to earn
1.50x  20
This works out to 13.333,
So at least 14 pizzas.
What happens when each side of an
inequality is multiplied or divided by
a negative number?
-6 < 11
Multiply each side by -1: -1(-6) < -1(11)
This inequality is false: 6 < -11
10  5
Divide each side by -5: 10  5
-5 -5
This inequality is false: -2  -1
The inequalities 6 < -11 and -2 > -1 are both false. However,
They would both be true if the inequality symbols were reversed.
Change < to > and change > to <.
6 > -11 TRUE
-2 < -1 TRUE
Key Concept:
Multiplication & Division
Properties (352)
Words: When you multiply or divide each of an inequality by the
same negative number, the inequality symbol must be
REVERSED for the inequality to remain true.
Symbols: For all numbers a, b, c, where c 0,
1. If a > b, then ac < bc and a < b
c
c
2. If a < b, then ac> bc and a > b
c c
Key Concept Continued:
» Examples:
7>1
-2(7) < -2(1)
-14 < -2
-4 < 16
Reverse the symbols-4  16
-4 -4
1 > -4
This is also true when using  and 
Example 3: Divide by a
Negative Number
» Solve each inequality and check your solution.
Then graph the solution on a number line.
15  -5b
Divide each side by -5 and reverse the symbol:
15  -5b
-5
-5
Check this result: -3  b or b  -3
You can check this result by replacing x in
the original equation with -3 or a number
less than -3
Check using -4:
15  -5(-4)
15  20 
See the board for the graph.
Example 3: Multiply by a
Negative Number
» Solve the inequality, check your solution
and graph the solution on a number line.
6> x
-7
Multiply each side by -7 and reverse the
symbol: -7(6) < x (-7)
-7
Check this result: -42  x or x > -42
Check by putting a number greater than -42 in the original
inequality.
Check using -35:
See graph on board.
6 > -35
= 6 > 5
-7
Your Turn!!
Solve, check and graph each
inequality
A.
s  -3.5
3
B. 15 > 3t
C. 13a  -26
D. 7  h
-14
(-3) s  -3.5(-3)
3
s  10.5
15  3t
3
3
5 > t or t  5
13a  -26
13
13
a  -2
(-14)7 
h (-14)
-14
-98  h or h  -98
»
Extra Practice Is By The Door On
Your Way Out!
» Don’t Let The Negative Signs Trip
You Up!!