learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or...
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![Page 1: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/1.jpg)
Learn to solve one-step inequalities by
adding or subtracting.
Course 2
11-5Solving Inequalities by
Adding or Subtracting
![Page 2: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/2.jpg)
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
![Page 3: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/3.jpg)
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
![Page 4: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/4.jpg)
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
![Page 5: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/5.jpg)
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
![Page 6: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/6.jpg)
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
![Page 7: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/7.jpg)
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
![Page 8: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/8.jpg)
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
![Page 9: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/9.jpg)
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
![Page 10: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/10.jpg)
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
![Page 11: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/11.jpg)
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
![Page 12: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/12.jpg)
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
![Page 13: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/13.jpg)
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
![Page 14: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/14.jpg)
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
![Page 15: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/15.jpg)
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
![Page 16: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/16.jpg)
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
![Page 17: Learn to solve one-step inequalities by adding or … to solve one-step inequalities by adding or subtracting. Course 2 ... solutions of equations, by isolating the ... Solving Inequalities](https://reader031.vdocuments.mx/reader031/viewer/2022022506/5abfc31a7f8b9ac6688b4ac1/html5/thumbnails/17.jpg)
Homework
11-5 Worksheet
Quiz corrections due Thursday