Transcript Section 02

7-2: Solving Inequalities by Using Multiplication and Division
OBJECTIVE:
You will solve inequalities by using multiplication and division.
The rules for multiplying and dividing both sides of an inequality are
essentially the same as for equations.
There is one key difference you must remember to do:
WHENEVER YOU MULTIPLY OR DIVIDE BOTH SIDES BY A
NEGATIVE NUMBER, YOU MUST SWITCH THE DIRECTION
OF THE INEQUALITY.
2<3
-6 < -3
2<3
-6 < -3
3(2) < 3(3)
-6  (3) < -3  (3) -3(2) < -3(3) -6  (-3) < -3  (-3)
6<9
-2 < -1
-6 < -9
2<1
Both statements are still true, so multiplying and dividing Both statements are now false. In order to get that back to
by a positive number did not affect the inequality symbol. true statement, the inequality sign must be flipped.
-6 > -9
2>1
© William James Calhoun, 2001
7-2: Solving Inequalities by Using Multiplication and Division
Le
EXAMPLE 1: Solve the inequality
7 .
1.5
Le
What is the variable?
7
Le
1.5
What is on the same side?
Now, since both sides were multiplied
1.5
by something, pause and ask yourself,
 Le 
1.5

1.5
7
  “Did I multiply both sides by a negative
How are they combined?


 1.5 
division
number?”
To undo…
The answer is no, so do not change the
Le  10.5
multiply both sides by 1.5
inequality sign.
{Le | Le  10.5}
x 3
 .
EXAMPLE 2: Solve
12 2
What is the variable?
Now, since both sides were multiplied
x
3




x
by something, pause and ask yourself,
12    12  
What is on the same side?
“Did I multiply both sides by a negative
12 
2


12
number?”
How are they combined?
x  18
The answer is no, so do not change the
division
To undo…
multiply both sides by 12
{x | x  18}
inequality sign.
© William James Calhoun, 2001
7-2: Solving Inequalities by Using Multiplication and Division
EXAMPLE 3: Solve -3w > 27.
-3w > 27
What is the variable?
-3 -3
w
What is on the same side?
w < -9
negative 3
How are they combined?
{w | w < -9}
multiplication
To undo…
divide both sides by -3
Now, since both sides were divided by
something, pause and ask yourself, “Did
I divide both sides by a negative
number?”
The answer is yes, so change the
inequality sign.
© William James Calhoun, 2001
7-2: Solving Inequalities by Using Multiplication and Division
EXAMPLE 4: Angelica Moreno is a sales representative for an
appliance distributor. She needs more than $5000 in weekly sales of a
particular TV model to qualify 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?
Moreno needs to have sales figures that total more than $5000 to win.
Her sales figures are based on how many she sells times the number she sells.
$250 times the number of TVs she sells gives her sales figure.
Let T be the number of TVs she sells, giving the inequality:
250(T)
>
5000
Rewrite and solve.
250 T > 5000
250 T > 5000
250
250
T > 20
Moreno needs to sell more than 20 TVs to win
the trip.
Note, selling 20 exactly will not earn her the trip,
it must be 21 or more.
© William James Calhoun, 2001
7-2: Solving Inequalities by Using Multiplication and Division
HOMEWORK
Page 396
#23 - 41 odd
© William James Calhoun, 2001