Download Page Solve Inequalities Using Multiplication and Division 6.2 Goal

Solve Inequalities Using Multiplication and Division
6.2 Goal • Solve inequalities using multiplication and division.
Warm-up:
1) Work with your group to complete the following tables.
INEQUALITY
MULTIPLY EACH SIDE
NEW INEQUALITY
BY:
3<4
2
6<8
2 > -3
3
-1 < 6
5
5>2
-1
1<7
-5
-8 > -10
-8
INEQUALITY
DIVIDE EACH SIDE BY:
NEW INEQUALITY
4<8
4
`1 < 2
12 > -15
3
-16 < 12
-4
15 > 5
-5
IS THE NEW ONE TRUE
OR FALSE?
TRUE
IS THE NEW ONE TRUE
OR FALSE?
TRUE
2) Based on what you observed, complete the following statement:
When both sides of an inequality are multiplied or divided by a ____________________ number, the
inequality is no longer true.
3) Work with your group to complete the following tables.
NEW INEQUALITY
5>2
-1
-5 > -2
1<7
-5
-8 > -10
-8
REWRITE BY
REVERSING THE
SYMBOL
-5 < -2
REVERSED
SYMBOL MAKE IT
TRUE OR FALSE?
YES
1
MULTIPLY EACH
SIDE BY:
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INEQUALITY
INEQUALITY
DIVIDE EACH
SIDE BY:
-16 < 12
-4
15 > 5
-5
NEW INEQUALITY
REWRITE BY
REVERSING THE
SYMBOL
REVERSED
SYMBOL MAKE IT
TRUE OR FALSE?
4) Based on what you observed, complete the following statement:
When both sides of an inequality are multiplied or divided by a ____________________ number, you
must _________________________________________________________________ to it true.
5) Describe what you discovered from this warm-up.
Solve the inequality.
6) 20x ≥ 5
7) -8x > -40
8) -9x ≤ 45
9) 7x < 21
______________________________________________________________________
6.2 Exploring Inequalities with Negative Coefficients
MULTIPLICATION PROPERTY OF INEQUALITY
Words
Multiplying each side of an inequality by a ______________ number produces an
___________________
______________________.
Multiplying each side of an inequality by a __________________ number and
________________ _______________________________ of the inequality symbol produces an
equivalent inequality.
If a < b and c < 0, then _________.
If a > b and c > 0, then _________.
If a > b and c < 0, then _________.
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This property is also true for inequalities involving ≤ and ≥ .
2
Algebra
If a < b and c > 0, then _________.
Example 1 - Solve an inequality using multiplication
y > 3.
Solve
Graph your solution.
9
Example 2 - Solve an inequality using multiplication
Solve
m
< 5.
−2
Graph your solution.
Checkpoint Solve the inequality. Graph your solution.
r
≤ 6
7
s
2) − > 0.4
4
3) n ≥ −2
−5
4) w < −0.8
6
1)
DIVISION PROPERTY OF INEQUALITY
Words Dividing each side of an inequality by a ________________ number produces an
_____________________ ______________________.
Dividing each side of an inequality by a ____________________ number and
____________________________________________ produces an equivalent inequality.
Algebra
If a < b and c < 0, then _____.
If a > b and c > 0, then _____.
If a > b and c < 0, then _____.
This property is also true for inequalities involving ≤ and ≥ .
Page
3
If a < b and c > 0, then _____.
Example 3 - Solve an inequality using division
Solve −4x < 36. Graph your solution.
Example 4 - Solve a real-world problem
Pizza Party You have a budget of $45 to buy pizza for a student council meeting. Pizzas cost $7.50
each. Write and solve an inequality to find the possible numbers of pizzas that you can buy.
Price per pizza
(dollars per
pizza)
•
Number of
pizzas
(pizzas)
≤
Budget amount
(dollars)
______
•
P
≤
______
___________
P ≤ ____
Write inequality.
Divide each side by _______.
Checkpoint Solve the inequality. Graph your solution.
6) 10n ≥ 140
5) 36<−9k
Page
4
7) In Example 4, suppose that you had a budget of $50 and each pizza
costs $8. Write and solve an inequality to find the possible numbers of
pizzas that you can buy.