11-5 Solving Inequalities by Adding and Subtracting

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpWrite 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

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

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.

Course 2

11-5 Solving Inequalities by Adding or Subtracting

Solve. Then graph the solution set on a number line.

Additional Example 1A: Solving Inequalities by Adding

A. n – 7 ≤ 15 n – 7 ≤ 15

+ 7 + 7

n ≤ 22

Add 7 to both sides.

Draw a closed circle at 22 then shade the line to the left of 22.

0 7 14 21 28 35–14 –7

Course 2

11-5 Solving Inequalities by Adding or Subtracting

Solve. Then graph the solution set on a number line.

Additional Example 1B: Solving Inequalities by Adding

B. a – 10 ≥ –3

a – 10 ≥ –3+ 10 +10

a ≥ 7

Add 10 to both sides.

Draw a closed circle at 7. 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

Solve. Then graph the solution set on a number line.

A. d – 12 ≤ –18 d – 12 ≤ –18

+ 12 + 12

d ≤ –6

Add 12 to both sides.

Draw a closed circle at –6 then shade the line to the left of –6.

Try This: Example 1A

–8 –6 –4 –2 0 2 4 6Course 2

11-5 Solving Inequalities by Adding or Subtracting

Solve. Then graph the solution set on a number line.

B. b – 14 ≥ –8

b – 14 ≥ –8+ 14 +14

b ≥ 6

Add 14 to both sides.

Draw a closed circle at 6. Then shade the line to the right.

–4 –2 0 2 4 6 8 10

Try This: Example 1B

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.

Course 2

11-5 Solving Inequalities by Adding or Subtracting

Solve. Check each answer.

Additional Example 2A: Solving Inequalities by Subtracting

A. d + 11 > 6d + 11 > 6

–11 –11

d > –5

Checkd + 11 > 6

0 + 11 > 6?

11 > 6?

Subtract 11 from both sides.

0 is greater than –5.Substitute 0 for d.

Course 2

11-5 Solving Inequalities by Adding or Subtracting

Solve. Check your answer.

Additional Example 2B: Solving Inequalities by Subtracting

B. b + 12 ≤ 19b + 12 ≤ 19

–12 –12

b 7

Checkb + 12 ≤ 19

6 + 12 19

18 19

Subtract 12 from both sides.

6 is less than 7.Substitute 6 for b.

≤?

?≤

≤

Course 2

11-5 Solving Inequalities by Adding or Subtracting

Solve. Check each answer.

A. c + 15 > 9c + 15 > 9

–15 –15

c > –6

Checkc + 15 > 9

0 + 15 > 9?

15 > 9?

Subtract 15 from both sides.

0 is greater than –6.Substitute 0 for c.

Try This: Example 2A

Course 2

11-5 Solving Inequalities by Adding or Subtracting

Solve. Check your answer.

B. a + 15 ≤ 20a + 15 ≤ 20

–15 –15

a 5

Checka + 15 ≤ 20

4 + 15 20

19 20

Subtract 15 from both sides.

4 is less than 5.Substitute 4 for a.

≤?

?≤

≤

Try This: Example 2B

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

Course 2

11-5 Solving Inequalities by Adding or Subtracting

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?

Additional Example 3: Meteorology Application

Let t represent the temperature increase fromlast year to this year.

–2 + t ≤ 13+2 +2

t ≤ 15

The temperature forecast for this year is at most15°F warmer than the temperature recorded last year.

Add 2 to both sides.

Course 2

11-5 Solving Inequalities by Adding or Subtracting

Try This: Example 3Last 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?

Insert Lesson Title Here

Let t represent the takeaway increase fromlast year to this year.

–8 + t ≤ 8

+8 +8

t ≤ 16

The takeaway ratio for this year will be at least16 greater this year than that recorded last year.

Add 8 to both sides.

Course 2

11-5 Solving Inequalities by Adding or Subtracting

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

Insert Lesson Title Here

p ≥ –24

k > 184. k + 47 > 65

13 15 17 19 21 23 25

x > 21

40 42 44 46 48 50 52•

z ≤ 46

Course 2

11-5 Solving Inequalities by Adding or Subtracting

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?

Insert Lesson Title Here

bus riders ≥ 24

Course 2

11-5 Solving Inequalities by Adding or Subtracting