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Solving Inequalities by Multiplying or Dividing

In this lesson, we explore solving inequalities involving multiplication and division. We start with a scenario where a small business sells CDs for $12 each and aims to reach a revenue of at least $84,000. By setting up the inequality (12c geq 84,000) and simplifying through division, we find that the business must sell at least 7,000 CDs. We also check the reasonableness of our answer, affirming that selling 7,000 CDs meets the revenue goal.

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Solving Inequalities by Multiplying or Dividing

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  1. > –2 p 3 p 3 p 3 (3) > –2(3)Multiply each side by 3. p > –6 Simplify. COURSE 3 LESSON 2-7 Solving Inequalities by Multiplying or Dividing Solve > –2. Graph the solution. 2-7

  2. > > > > – – – – Words number of CDs • $12 is at least $84,000 Let c = the number of CDs. Inequality c • 12 84,000 12c 84,000 12c 12 84,000 12 Divide each side by 12. c 7,000 Simplify. COURSE 3 LESSON 2-7 Solving Inequalities by Multiplying or Dividing A small business sells each CD of its game software for $12. How many CDs must they sell to meet the goal of at least $84,000? 2-7

  3. COURSE 3 LESSON 2-7 Solving Inequalities by Multiplying or Dividing (continued) The business must sell at least 7,000 CDs. Check for Reasonableness The answer makes sense because 7,000 • 12 is 84,000, and any number over 7,000 multiplied by 12 is a number greater than 84,000. 2-7

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