Solving Inequalities by
11-5 Adding and Subtracting
Warm Up
Problem of the Day
Lesson Presentation
Course 2
Solving Inequalities by
11-5 Adding or Subtracting
Warm Up
Write the inequality for each situation.
There are at least 28 days in a
month. days in a month ≥ 28
1.
2.
The temperature is above 72°.
temperature > 72°
At most 9 passengers can ride
in the van. passengers ≤ 9
3.
Course 2
Solving Inequalities by
11-5 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
Solving Inequalities by
11-5 Adding or Subtracting
Learn to solve one-step inequalities by
adding or subtracting.
Course 2
Solving Inequalities by
11-5 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
Solving Inequalities by
11-5 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
n
≤ 22
Add 7 to both sides.
Draw a closed circle at 22 then
shade the line to the left of 22.
–14
Course 2
–7
0
7
14
21
28
35
Solving Inequalities by
11-5 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
a
–4
Course 2
≥
–2
Add 10 to both sides.
7
0
Draw a closed circle at 7.
Then shade the line to the right.
2
4
6
8
10
Solving Inequalities by
11-5 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
d
≤
–6
Add 12 to both sides.
Draw a closed circle at –6 then
shade the line to the left of –6.
–8
Course 2
–6
–4
–2
0
2
4
6
Solving Inequalities by
11-5 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
b
–4
Course 2
≥
–2
Add 14 to both sides.
6
0
Draw a closed circle at 6.
Then shade the line to the right.
2
4
6
8
10
Solving Inequalities by
11-5 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
Solving Inequalities by
11-5 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
Course 2
0 + 11
?
>
6
11
?
>
6
0 is greater than –5.
Substitute 0 for d.
Solving Inequalities by
11-5 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
Course 2
6 + 12
?
≤
19
18
?
≤
19
6 is less than 7.
Substitute 6 for b.
Solving Inequalities by
11-5 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
Course 2
0 + 15
?
>
9
15
?
>
9
0 is greater than –6.
Substitute 0 for c.
Solving Inequalities by
11-5 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
Course 2
4 + 15
?
≤
20
19
?
≤
20
4 is less than 5.
Substitute 4 for a.
Solving Inequalities by
11-5 Adding or Subtracting
Helpful Hint
When checking your solution, choose a number
in the solution set that is easy to work with.
Course 2
Solving Inequalities by
11-5 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
t ≤ 15
Add 2 to both sides.
The temperature forecast for this year is at most
15°F warmer than the temperature recorded last year.
Course 2
Solving Inequalities by
11-5 Insert
Title Here
Adding Lesson
or Subtracting
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.
Course 2
Solving Inequalities by
11-5 Adding
Insert or
Lesson
Title Here
Subtracting
Lesson Quiz: Part 1
Solve. Then graph each solution set on a
number line.
x > 21
1. x – 4 > 17
2. z – 27 ≤ 19
13
15
17
19
21
23
25
40
42
44
46
48
50
52
z ≤ 46
Solve.
3. p + 18 ≥ –6
p ≥ –24
4. k + 47 > 65
k > 18
Course 2
•
Solving Inequalities by
11-5 Adding
Insert or
Lesson
Title Here
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?
bus riders ≥ 24
Course 2