course 2: inequalities
DESCRIPTION
Course 2: Inequalities. Objectives: To determine whether a number is a solution of an inequality To graph inequalities on the number line To write inequalities. Inequalities. An inequality is a mathematical sentence containing >, , < . Inequalities. Inequalities. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/1.jpg)
Course 2: InequalitiesObjectives: •To determine whether a number is a solution of an inequality•To graph inequalities on the number line•To write inequalities
![Page 2: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/2.jpg)
Inequalities• An inequality is a mathematical
sentence containing >, <, >, <.
![Page 3: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/3.jpg)
Inequalities
Words
- is less than
- is greater than
-is less than or equal to- is at most
-is greater than or equal to-is at least
Symbols < > < >
![Page 4: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/4.jpg)
Inequalities• Any number that makes an
inequality true is a solution of the inequality.
• Inequalities have many solutions.
• Example: x > 4 • List 4 possible solutions. 4.5, 5, 7,
12.5
![Page 5: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/5.jpg)
Example 2The solutions are shown by shading a number line. Example: x > 4
3 4 5 6 7
![Page 6: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/6.jpg)
Example 1Determine whether each number is a solution of
a) 3
x 7.
b) -2c) 9
d) 7
yes, because 3 is less than 7yes, because -2 is less than 7no, because 9 is not less than or equal to 7yes, because 7 is equal to 7
![Page 7: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/7.jpg)
1)Graph m > 3 on a number line.
1 2 3 4 5
![Page 8: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/8.jpg)
2)Graph k < -2 on a number line.
-3 -2 -1 0 1
![Page 9: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/9.jpg)
3)Graph h > 3 on a number line.
0 1 2 3 4
![Page 10: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/10.jpg)
4)Graph k < -2 on a number line.
-3 -2 -1 0 1
![Page 11: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/11.jpg)
Solving One-Step Inequalities by Adding or
Subtracting• 1) x + 4 > 8 - 4 - 4
x > 4
![Page 12: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/12.jpg)
Check x + 4 > 8• Solution: x > 4
• Substitute a value that is greater than 4 for x.
5 + 4 > 8 9 > 8 This is a true statement.
![Page 13: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/13.jpg)
Graph x > 4
1 2 3 4 5
![Page 14: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/14.jpg)
Solving One-Step Inequalities by Adding or
Subtracting• 2) c - 3 < 2 + 3 + 3
c < 5
![Page 15: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/15.jpg)
Check c – 3 < 2• Solution: c < 5
• Substitute a value that is less than or equal to 5 for c.
5 – 3 < 2 2 < 2 This is a true statement.
![Page 16: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/16.jpg)
2 3 4 5 6
Graph c < 5 on a number line.
![Page 17: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/17.jpg)
Solving One-Step Inequalities by Adding or
Subtracting• 3) d - 4 < -2 + 4 + 4
d < 2
![Page 18: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/18.jpg)
Check d – 4 < -2• Solution: d < 2
• Substitute a value that is less than 2 for d.
1 – 4 < -2 -3 < -2 This is a true
statement.
![Page 19: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/19.jpg)
Graph d < -2.
-5 -4 -3 -2 -1
![Page 20: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/20.jpg)
Solving One-Step Inequalities by Adding or
Subtracting• 4) a - 2 > 6 + 2 + 2
a > 8
![Page 21: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/21.jpg)
Check a - 2 > 6• Solution: a > 8
• Substitute a value that is greater than or equal to 8 for a.
8 - 2 > 6 6 > 6 This is a true statement.
![Page 22: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/22.jpg)
Graph a > 8.
5 6 7 8 9
![Page 23: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/23.jpg)
Solving One-Step Inequalities by Adding or
Subtracting• 5) p - 7 > 0 + 7 + 7
p > 7
![Page 24: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/24.jpg)
Check p - 7 > 0• Solution: p > 7
• Substitute a value that is greater than 7 for p.
8 - 7 > 0 1 > 0 This is a true statement.
![Page 25: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/25.jpg)
Graph p > 7
4 5 6 7 8
![Page 26: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/26.jpg)
Solving One-Step Inequalities by Adding or
Subtracting• 6) j + 5 < 2 - 5 - 5
j < -3
![Page 27: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/27.jpg)
Check j + 5 < 2• Solution: j < -3
• Substitute a value that is less than or equal to -3 for c.
-3 + 5 < 2 2 < 2 This is a true statement.
![Page 28: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/28.jpg)
-5 -4 -3 -2 -1
Graph j < -3 on a number line.
![Page 29: Course 2: Inequalities](https://reader035.vdocument.in/reader035/viewer/2022062501/5681601e550346895dcf1e88/html5/thumbnails/29.jpg)
Review