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3-3 Solving Inequalities by Multiplying or Dividing

Video Tutor Help Solving Inequalities by Multiplying or Dividing Khan Academy Solving one-step whole number inequalities by dividingSolving one-step whole number inequalities by dividing (3-3) Solving one-step whole number inequalities by multiplyingSolving one-step whole number inequalities by multiplying (3-3)

Video Tutor Help Graphing solutions to one variable inequalities Writing an inequality from a graph Writing inequalities Solving one-step whole number inequalities by adding Solving one-step whole number inequalities by subtracting Solving one-step whole number inequalities by dividing Solving one-step whole number inequalities by multiplication

Worksheets Daily Notetaking Guide Worksheets Version A Practice, Guided Problem Solving Lesson 3-3 Practice 3-3 Guided Problem Solving 3-3

Vocabulary Practice Vocabulary (Electronic) Flash Cards Operations with Fractions Vocabulary 3A: Graphic Organizer Vocabulary 3B: Reading Comprehension Vocabulary 3C: Reading/Writing Math Symbols Vocabulary 3D: Visual Vocabulary Practice Vocabulary 3E: Vocabulary C Vocabulary 3F: Vocabulary Review Puzzle

Additional Lesson Examples Step-by-Step Examples Lesson 3-3

Lesson Readiness Lesson Quiz Problem of the Day Lesson 3-3

Note When multiplying or dividing by a negative : reverse the inequality symbol.

Common misconception Do not reverse the inequality sign just because there is a negative sign in the inequality. Only reverse the sign when you multiply or divide by a negative number.

Example 5-1a Solve. Check your solution. Divide each side by 9. Simplify. Write the inequality. Answer: The solution is. You can check this solution by substituting 6 or a number less than 6 into the inequality. Multiply or Divide by a Positive Number

Example 5-3a Solve and check your solution. Then graph the solution on a number line. Write the inequality. Answer: Check this result. Divide each side by –9 and reverse the symbol. Multiply or Divide by a Negative Number

Example 5-3a Graph the solution,. Answer:

Example 7-1a Check your solution. Answer: The solution is You can check this solution by substituting numbers less than –5 into the inequality. Write the inequality. Simplify. Divide each side by 6. Solve Divide by a Positive Number

Example 7-1b Check your solution. Answer: Solve

Example 7-4a Write the inequality. Check this result. Divide each side by –4 and reverse the inequality symbol. Answer: Graph the solution, Solve Then graph the solution on a number line. - Multiply or Divide by a Negative Number

Example 7-4b Answer: Then graph the solution on a number line. Solve

Solve 6a –18. Graph the solution. LESSON 3-3 a –3Simplify. < – 6a –18 < – 6a –18 Divide each side by 6. 6 < – < – Solving Inequalities by Multiplying or Dividing Additional Examples

A woodworker makes a profit of $30 on each picture frame that is sold. How many frames must the woodworker sell to make a profit of at least $500? LESSON 3-3 Words number of times profit on is at least total frames each frame profit Let f = number of frames. Inequality f > – f > – Solving Inequalities by Multiplying or Dividing Additional Examples

Answer: The solution is. You can check this solution by substituting a number greater than 36 into the inequality. Example 5-1a Solve. Check your solution. Write the inequality. Multiply each side by 9. Simplify. Multiply or Divide by a Positive Number

Example 5-3a Solve and check your solution. Then graph the solution on a number line. CheckYou can check your result by replacing x in the original inequality with a number less than –35. Answer: Check this result. Multiply each side by –5 and reverse the symbol. Write the inequality. Multiply or Divide by a Negative Number

Example 5-3a Answer: Graph the solution,.

Example 7-2a and check your solution. Then graph Write the inequality. Simplify. Multiply each side by 2. the solution on a number line. The solution is You can check this solution by substituting 18 and a number greater than 18 into the inequality. Solve Multiply by a Positive Number

Example 7-2a Answer: Graph the solution,

(continued) The woodworker must sell at least 17 frames. LESSON 3-3 f 16.6Simplify. > – f 17Round the answer up to find a whole number. > – Divide each side by 30. > – f Solving Inequalities by Multiplying or Dividing Additional Examples

Solve < –12. LESSON 3-3 b > 36Simplify. –3 > –3 –12 Multiply each side by –3. Reverse the direction of the symbol. b –3 b –3 < –12 b –3 Solving Inequalities by Multiplying or Dividing Additional Examples