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Learn to solve one-step inequalities by
adding or subtracting.
Course 2
11-5Solving 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
11-5Solving 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
11-5Solving 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
11-5Solving 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 6
Course 2
11-5Solving 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
11-5Solving 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
11-5Solving Inequalities by
Adding or Subtracting
Solve. Check each answer.
Additional Example 2A: Solving Inequalities by
Subtracting
A. d + 11 > 6
d + 11 > 6
–11 –11
d > –5
Check
d + 11 > 6
0 + 11 > 6?
11 > 6?
Subtract 11 from both sides.
0 is greater than –5.Substitute 0 for d.
Course 2
11-5Solving Inequalities by
Adding or Subtracting
Solve. Check your answer.
Additional Example 2B: Solving Inequalities by
Subtracting
B. b + 12 ≤ 19
b + 12 ≤ 19
–12 –12
b 7
Check
b + 12 ≤ 19
6 + 12 19
18 19
Subtract 12 from both sides.
6 is less than 7.Substitute 6 for b.
≤?
?≤
≤
Course 2
11-5Solving Inequalities by
Adding or Subtracting
Solve. Check each answer.
A. c + 15 > 9
c + 15 > 9
–15 –15
c > –6
Check
c + 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
11-5Solving Inequalities by
Adding or Subtracting
Solve. Check your answer.
B. a + 15 ≤ 20
a + 15 ≤ 20
–15 –15
a 5
Check
a + 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
11-5Solving 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
11-5Solving 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
11-5Solving Inequalities by
Adding 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?
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
11-5Solving 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
11-5Solving 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
11-5Solving Inequalities by
Adding or Subtracting
Homework
11-5 Worksheet
Quiz corrections due Thursday
