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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