3-3 Solving Inequalities Multiply or Divide.notebook

33 Solving Inequalities Multiply or Divide.notebook
3-3: Solving Inequalities Using
Multiplication and Division
Objective:
• You will be able to find solutions for inequalities by solving using multiplication and division.
Definitions:
equation
inequality
Solving an ___________________ is like solving an ________________.
ALONE
variable
The “goal” is to get the ________________ ___________ on one side of the inequality.
The “rules” are the same as when solving equations: multiply
• If you __________________ one side of the inequality by a number, multiply
you have to __________________ the other side of the inequality by the same number.
divide
• If you ______________ one side of the inequality by a number, you have
divide
to ______________ the other side of the inequality by the same number.
1
33 Solving Inequalities Multiply or Divide.notebook
Practice Problems:
Solve each inequality and graph the solution.
1.
10
9
8
7
6
5 4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
2.
10
9
8
7
6
5 4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Investigation for 33
Multiplying Each Side of an Inequality
Consider the inequality 4 > 1.
1. Complete each statement below by replacing each with <, >, or =.
4 • 3 1 • 3
4 • 2 1 • 2
4 • 1 1 • 1
4 • 1 1 • 1
4 • 0 1 • 0
4 • 2 1 • 2
4 • 3 1 • 3
2. What happens to the inequality symbol when you multiply each side by a positive number?
3. What happens to the inequality symbol when you multiply each side by zero?
4. What happens to the inequality symbol when you multiply each side by a negative number?
2
33 Solving Inequalities Multiply or Divide.notebook
The special “rules” are:
negative
multiply
• If you ______________ one side of the inequality by a ______________ flip
number, you must __________ the inequality sign.
negative
divide
• If you ______________ one side of the inequality by a ______________ flip
number, you must __________ the inequality sign.
3.
10
9 8 7
6
5 4 3
2
1
0
1
2
3
4
5
6
7
8
9
10
4.
10
9 8 7
6
5 4 3
2
1
0
1
2
3
4
5
6
7
8
9
10
3
33 Solving Inequalities Multiply or Divide.notebook
5.
10
9 8 7
6
5 4 3
2
1
0
1
2
3
4
5
6
7
8
9
10
6.
10
9 8 7
6
5 4 3
2
1
0
1
2
3
4
5
6
7
8
9
10
7.
10
9 8 7
6
5 4 3
2
1
0
1
2
3
4
5
6
7
8
9
10
8.
10
9 8 7
6
5 4 3
2
1
0
1
2
3
4
5
6
7
8
9
10
4
33 Solving Inequalities Multiply or Divide.notebook
Solve each situation using an inequality.
9.
Interact voted to buy food for a local food bank. A case of spaghetti sauce costs $13.75. What is the greatest number of cases of sauce Interact can buy if they have at most $216 to spend?
10. The band is selling calendars to earn money for a trip. They earn $.90 on each calendar they sell. Their goal is to earn at least $250. What is the fewest number of calendars they need to sell to reach their goal?
5

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