Solving Inequalities by Adding and Subtracting 11-5 Solving Inequalities by Adding and Subtracting Course 2 Warm Up Problem of the Day Lesson Presentation

Solving Inequalities by Adding or Subtracting Course 2 11-5 Solving Inequalities by Adding or Subtracting Warm Up Write the inequality for each situation. 1. There are at least 28 days in a month. 2. The temperature is above 72°. 3. At most 9 passengers can ride in the van. days in a month ≥ 28 temperature > 72° passengers ≤ 9

Solving Inequalities by Adding or Subtracting Course 2 11-5 Solving Inequalities by Adding or Subtracting Problem of the Day Daryl gave the clerk less than $20 for a CD and received change of at least $5. He ended up with the CD and less money than he started with. Write a compound inequality to show what C, the cost in dollars of the CD, could have been. 0 < C < 15

Learn to solve one-step inequalities by adding or subtracting. Course 2 11-5 Solving Inequalities by Adding or Subtracting Learn to solve one-step inequalities by adding or subtracting.

Course 2 11-5 Solving Inequalities by Adding or Subtracting When you add or subtract the same number on both sides of an inequality, the resulting statement will still be true. –2 < 5 +7 +7 5 < 12 You can find solution sets of inequalities the same way you find solutions of equations, by isolating the variable.

Additional Example 1A: Solving Inequalities by Adding Course 2 11-5 Solving Inequalities by Adding or Subtracting Additional Example 1A: Solving Inequalities by Adding Solve. Then graph the solution set on a number line. A. n – 7 ≤ 15 n – 7 ≤ 15 + 7 + 7 Add 7 to both sides. n ≤ 22 Draw a closed circle at 22 then shade the line to the left of 22. 7 14 21 28 35 –14 –7

Additional Example 1B: Solving Inequalities by Adding Course 2 11-5 Solving Inequalities by Adding or Subtracting Additional Example 1B: Solving Inequalities by Adding Solve. Then graph the solution set on a number line. B. a – 10 ≥ –3 a – 10 ≥ –3 + 10 +10 Add 10 to both sides. a ≥ 7 Draw a closed circle at 7. Then shade the line to the right. –4 –2 0 2 4 6 8 10

Solving Inequalities by Adding or Subtracting Course 2 11-5 Solving Inequalities by Adding or Subtracting Try This: Example 1A Solve. Then graph the solution set on a number line. A. d – 12 ≤ –18 d – 12 ≤ –18 + 12 + 12 Add 12 to both sides. d ≤ –6 Draw a closed circle at –6 then shade the line to the left of –6. –8 –6 –4 –2 0 2 4 6

Solving Inequalities by Adding or Subtracting Course 2 11-5 Solving Inequalities by Adding or Subtracting Try This: Example 1B Solve. Then graph the solution set on a number line. B. b – 14 ≥ –8 b – 14 ≥ –8 + 14 +14 Add 14 to both sides. b ≥ 6 Draw a closed circle at 6. Then shade the line to the right. –4 –2 0 2 4 6 8 10

Course 2 11-5 Solving Inequalities by Adding or Subtracting You can see if the solution to an inequality is true by choosing any number in the solution set and substituting it into the original inequality.

Additional Example 2A: Solving Inequalities by Subtracting Course 2 11-5 Solving Inequalities by Adding or Subtracting Additional Example 2A: Solving Inequalities by Subtracting Solve. Check each answer. A. d + 11 > 6 d + 11 > 6 –11 –11 Subtract 11 from both sides. d > –5 Check d + 11 > 6 0 + 11 > 6 ? 0 is greater than –5. Substitute 0 for d. 11 > 6 ?

Additional Example 2B: Solving Inequalities by Subtracting Course 2 11-5 Solving Inequalities by Adding or Subtracting Additional Example 2B: Solving Inequalities by Subtracting Solve. Check your answer. B. b + 12 ≤ 19 b + 12 ≤ 19 –12 –12 Subtract 12 from both sides. b 7 ≤ Check b + 12 ≤ 19 6 + 12 19 ≤ ? 6 is less than 7. Substitute 6 for b. 18 19 ? ≤

Solving Inequalities by Adding or Subtracting Course 2 11-5 Solving Inequalities by Adding or Subtracting Try This: Example 2A Solve. Check each answer. A. c + 15 > 9 c + 15 > 9 –15 –15 Subtract 15 from both sides. c > –6 Check c + 15 > 9 0 is greater than –6. Substitute 0 for c. 0 + 15 > 9 ? 15 > 9 ?

Solving Inequalities by Adding or Subtracting Course 2 11-5 Solving Inequalities by Adding or Subtracting Try This: Example 2B Solve. Check your answer. B. a + 15 ≤ 20 a + 15 ≤ 20 –15 –15 Subtract 15 from both sides. a 5 ≤ Check a + 15 ≤ 20 4 + 15 20 ≤ ? 4 is less than 5. Substitute 4 for a. 19 20 ? ≤

Solving Inequalities by Adding or Subtracting Course 2 11-5 Solving Inequalities by Adding or Subtracting When checking your solution, choose a number in the solution set that is easy to work with. Helpful Hint

Additional Example 3: Meteorology Application Course 2 11-5 Solving Inequalities by Adding or Subtracting Additional Example 3: Meteorology Application Last year, the low temperature for March 1 was –2°F. This year the forecast calls for a low of at most 13°F on that day. At most, how many degrees warmer is the temperature forecast to be on March 1 this year than last year? Let t represent the temperature increase from last year to this year. –2 + t ≤ 13 +2 +2 Add 2 to both sides. t ≤ 15 The temperature forecast for this year is at most 15°F warmer than the temperature recorded last year.

Insert Lesson Title Here Course 2 11-5 Solving Inequalities by Adding or Subtracting Insert Lesson Title Here Try This: Example 3 Last year, the football team had 8 more giveaways than takeaways or –8. This year they improved to having 8 more takeaways than giveaways or +8. If they have no more giveaways in their last game, their improvement over last year will be at least how much? Let t represent the takeaway increase from last year to this year. –8 + t ≤ 8 +8 +8 Add 8 to both sides. t ≤ 16 The takeaway ratio for this year will be at least 16 greater this year than that recorded last year.

Insert Lesson Title Here Course 2 11-5 Solving Inequalities by Adding or Subtracting Insert Lesson Title Here Lesson Quiz: Part 1 Solve. Then graph each solution set on a number line. 1. x – 4 > 17 2. z – 27 ≤ 19 Solve. 3. p + 18 ≥ –6 13 15 17 19 21 23 25 x > 21 40 42 44 46 48 50 52 • z ≤ 46 p ≥ –24 4. k + 47 > 65 k > 18

Insert Lesson Title Here Course 2 11-5 Solving Inequalities by Adding or Subtracting Insert Lesson Title Here Lesson Quiz: Part 2 Solve. 5. There are at least 17 more bus riders than walkers in a class. If there are 7 walkers, how many bus riders are there? bus riders ≥ 24