Transcript 3-3 PPT Inequalities using Multiplication and Division

Section 3-3 Solve Inequalities using Multiplication & Division
SPI 22N: identify the graphical representation of the solution to a one variable
inequality
Objectives:
• Use multiplication and division to solve inequalities
Consider the inequality 4 > 1.
4∙3 > 1∙3
1. Complete each statement at the right
with the appropriate inequality sign.
4∙2 > 1∙2
2. What happens to the symbol when
you multiply each side by a positive
number?
4∙0 = 1∙0
3. What happens to the symbol when
you multiply each side by 0?
4. What happens to the symbol when
you multiply each side by a negative
number?
4∙1 > 1∙1
4 ∙ -1 < 1 ∙ -1
4 ∙ -2 < 1 ∙ -2
4 ∙ -3 < 1 ∙ -3
Properties of Inequalities
Multiplication Property of Inequality:
For every real number a and b, and for c < 0
if a > b then ac < bc . . . and . . .
if a < b, then ac > bc
If c > 0, solve like an equality.
If a = 4, b = 2 and c = -2 . . . Then . . .
4 > 2 and 4(-2) < 2(-2)
Properties of Inequalities
Division Property of Inequality:
For every real number a and b, and for c < 0
if a > b then a < b . . . and . . .
c c
if a < b, then a > b
c c
If c > 0, solve like an equality.
If a = 4, b = 2 and c = -2 . . . Then . . .
4 > 2 and 4 < 2
-2 -2
Solve using the Properties of Inequalities
Solve the inequality
 4c  24
 4c 24

4 4
c  6
Since you have to divide by a negative
number, change the inequality sign
Simplify
Solve using the Properties of Inequalities
Solve the inequality
4
y0
3
3 4
3
  y  0 
4 3
4
y0
Multiply each side by the reciprocal of
the coefficient of y. Do not change the
sign, because you are not multiplying
by a negative value.
Simplify
Solve using the Properties of Inequalities
Your family budgets $160 to spend on fuel for a trip. How
many times can they fill the car’s gas tank if it cost $25
each time?
Define a variable for the unknown:
x = number of times car can be filled
Write an Inequality:
25x ≤ 160
Solve the Inequality
25x ≤ 160
25
25
x ≤ 6.4
Answer the question:
The car can be filled at least 6 times.